Good Afternoon.
First I would like to say that I am sure that you are more knowledgeable about the use of PC's than you give yourself credit for. And being willing to ask for help is always a good start, in any situation in life.
I would just say that a few more details about your PC would of been nice but I will try to offer help as best I can.
Now I am going to make a few assumptions before I start offering ideas and I would like to apologise if any of these assumptions cause offence or harm in anyway.
Here is what I will assume in an attempt to help you. This PC is a standard form factor Dell desktop PC. The PC is owned 100% by you. You are the main, if not sole, user of this PC. This PC is more than 18 months old. You did not take out a extended warranty or service plan on this PC. You do not want to spend too much money on trying to sort your problem and finally that you will not be using this speed up process as a springboard to using/running some very new software. You would just like to be able to have your PC operate in a manner more reminiscent of it when it was new.
OK, with all those in mind. Lets start cleaning! 
First I would like to suggest that we start with some actual physical cleaning. Begin by printing out this post for reference to when your PC is turned off (If you find that what I have written may help you that is!). PLEASE NOTE THAT THE REMOVAL OF YOUR PC CASE WILL MOST LIKELY VOID ANY WARRANTY THAT YOU MAY STILL HAVE REMAINING ON IT. Then please turn off your PC, monitor, speakers and printer. Once everything is turned off, remove all the power cables from their wall sockets, switching off any sockets before removing any cables (if applicable to you). Once all the power cables have been removed from their sockets move around to the back of your PC. Start to unplug every cable from the back of your PC: I would suggest that you start with the power cables which are normally located at the top of the box. Please be mindful of the fact that plugging the cables back in later may be a bit more complicated so you may wish to take a picture of the back of your PC with a digital camera for reference later (you could study the picture on the screen of the camera for a basic idea of where the cables go) and you may also wish to mark each cable with a small piece of tape marked with the name of the item that it is attached too. Also please note that some cables may need you to undo some screws that are holding them into the PC. Most commonly this the cable for the monitor. These can be undone without the aid of tools.
Once all the cables are clear of the box lift the box to place where it is at a comfortable height to work on and is well lit. For this next part you will need a screwdriver, most likely a Phillips (Crosshead). Around the edge of the rear of the box you will see a series of screws. Once you have removed all the screws plus any warranty stickers or plastic cables you can remove the lid of your PC by sliding or lifting it off, or a combination of both!
Once the cover is off clean all the vent holes in the cover with a cloth making sure to remove as much dust as you can see on the case. Now turn your attention to the inners of the PC. You may see several fans around the insides depending on the specifications of your PC. Do not attempt to remove any dust that you see around these fans with any sort of cloth or duster, this will just cause more problems than it solves. I use a standard vacuum cleaner on its lowest power setting and very quickly wave the nozzle over the fans to remove as must dust as possible. DO NOT hold the nozzle of the cleaner up against any fans or circuit boards in the case for any sustained period of time. Clean as much dust and fluff out of the case as you can.
Shut the case and replace the screws. Place the PC back in its place, reattach the cables double checking that they are all in securely and correctly. Once you are happy with that please restart your PC.
Now "drivers". These are pieces of software code that control the interaction between various pieces of hardware and software that go to make up your PC. I assume that you keep up-to-date with your Windows XP updates. "Drivers" will be pieces of software not totally unlike the updates that you download under the Windows update function. Once a piece of hardware is realised to the public the company that make it normally releases updates to the software that manages it, the "driver", as a way of either fixing things like compatibility problems, or to boost it's actual performance. "Drivers" can be found for nearly every single PC peripheral around today. From the simplest mouse to the latest, greatest, graphics card, they all have them! I have found that an issue that can cause some worries when confronting "drivers" is that the new driver can cause more problems that it solves. Yes they can, but it also an easy problem to rectify. OK so I hope that helped and did not confuse the situation any more.
What drivers should you be interested in? Where do you get the ones you want? OK, for a start, make a note on a piece of paper of the manufactures name and the model number of any piece of hardware that you have plugged into your PC. A big one might be a printer. I have an old HP printer, it's a HP PSC1315. Now the "driver" for this comes as part of the software that is on the CD that came with the printer. I have a web cam, a Logitech. I feel that unless you have upgraded your keyboard or mouse with relatively expensive models then the "drivers" for these can be ignored. Do you have a scanner? A bar code reader? Do you connect your mobile phone to your PC via a cable? An external hard drive? These are all things to make a note of.
From here on it gets a bit in-depth. Let's pick web cameras for a start. The "driver" for mine, like the printer, contained within the actual software bundle that came with it. When I installed the software it placed a small icon of a web camera in the windows Task bar alongside my clock. To see if there is an update for the software, and hence the "driver", I just right click on the camera icon and select "Check for Updates". You will find that if you have installed software for a specific piece of hardware from a CD/DVD then most often it would of place a folder in your "All Programs" list and that this folder may contain an option for checking for software/"driver" updates. If not just starting the software that controls the hardware will give you a chance to check for updates, often by clicking on the menus. Which menu it is can very widely! Now if this all seems to be a bit much, you can just type the name and model number of one of your peripherals into your favoured search engine and then go through, for example, the manufactures support site. You may have to make a selection from a series of drop down boxes/menus to get to the page that covers your peripheral but most sites these days are easy to navigate for anyone who has used the web for more than 10minutes!
From here you will most often find software/driver upgrades. But here is a point that I will raise again during the post. Do you need to update the software for the peripheral, or just the driver? If you are given the choice that is! I like to explain that in the quest to give an older PC a speed up, you may not want to install larger more complex software that could indeed slow the PC down even more. Take my printer for example. The software, HP Director, has gone through many changes since I got the printer so that now I would say that is almost unrecognisable to anyone familiar to the version that I installed over three years ago. So what do you do? Well I can only offer pointers here. If your use of any given peripheral is largely dependant on using the software that came with it, then where possible just update the driver. If new software exists for a peripheral then look what has been changed on it compared to the version that you run (See what's new / Compare), do you want/need any of this? Again I would say that as your are doing this exercise to speed up a PC unless the programme specifically states a greatly enhanced speed of operation, then stick with what you got!
So far I have talked about external hardware, but where the term driver really comes into its own is in connection with the hardware inside the PC! And where they get really fun! The most common driver to get updated in my experience is the one that controls the graphics card or chipset. And one that I would really recommend that you update. So which graphics card/chipset do you have? Right if you don't know or would like some more specific information then I would point you in the direction of Ccleaner:
http://www.download.com/CCleaner/3000-2144_4-10315544.html?tag=lst-1&cdlPid=10837066
Download and install this. Open the program and at the top right of the screen next to the large red letter C with the blue paint brush on it you will see some basic information about your system. It should show your operating system, name and version, your name and Model of Processor, the amount of System RAM and your graphics card name and model/series number!! This bit of software will come in very handy later in my reply as well!
So now you have the name of your graphics card/chipset. Type the information into your favourite search engine and head to the manufactures website. From there head over to the support page and most likely using a set of drop down boxes/menus navigate your way to the relevant page and here I would suggest that you take the latest software and driver. Most likely the driver will come as part of the latest version of the software so just take the software! Once it has downloaded, shut all other running apps, install the new driver, and if prompted restart your PC!
And right there you are off to a great start with speeding up your PC. Most of the dust has been cleaned out of it, and your graphics drivers are up to date! If you feel that you would like to update any more internal PC hardware drivers then you need to go the Windows Control Panel. Double click on System . The first tab on the box that comes up, called General will give you some more information about your PC, note this information on a bit of paper and keep it too hand for any future technical support requests! Look for a tab called Hardware, click on it. The click Device Manager. The next box is where you will be able to discover the names of most of the components found inside your PC. To see the names of any components just click on the plus signs at the edge of the box. Clicking on any the names that appear on here will enable you to find out all the relevant information about a devices driver! I feel that you would not need to worry about updating any other drivers but if you have been getting warning messages about drivers then here is where to find the name of the offending part, search for it, and follow the instructions for the graphics card bit.
As most people have said already, keeping a clean PC is the best way to keeping a fast PC. And I think that Ccleaner is the best for helping here. Now many people have already talked about using Windows utilities to clean up your PC but I feel the the software mentioned gives you more control. If as I said above I assume that you are the sole user of this PC then there is a fair chance that depending on your surfing habits you may have set certain websites to remember your login details and just using the windows tool to clean things can delete all of these! You may or may not find this annoying depending on your abilities to remember passwords and your feelings about online security. One benefit that you can get from Ccleaner is that it gives you the option to clean up your internet browsing history and associated mess while still leaving the cookies for any site that you feel you can trust with information intact. In Ccleaner, under the Options window you will see a box called Cookies, click on this and you will be presented with two columns, Cookies to Delete and Cookies to Keep. Use the arrow boxes located mid screen between the two columns to move any cookies that you want around. Ccleaner gives you plenty of options for the actual cleaning of your machine, and I will leave you to set it up as you feel bests suit you. I would recommend that when you use the cleaner function the first time you ensure that every box under both windows and the applications tabs are ticked, and then when this has run, click on the registry button and run the registry cleaner. I feel that it can clean up more than enough of the problems associated with registry type things. I have used this several hundred times and never had a problem with the registry cleaner deleting an incorrect file but I always use the backup changes to the registry function! And I suggest you do the same.
Also if your PC suffers from annoying programmes that insist on loading into your taskbar when your machine boots, Ccleaner can also show you all the programmes that boot themselves at Start up. You can delete any that you do not want from this list safe in the knowledge that it will not break the full programme if you still need that. Also the Un-installer featured on Ccleaner is very good and somewhat more comprehensive in my opinion that the one that Windows has. Both of these options can be found by clicking on the tools button on the left of the screen.
Once Ccleaner is tweaked to your liking then just get into the habit of running it once a day. You also want to de-fragment your hard drive. Use the windows one found under Start->All Programs->Accessories->System Tools. I would suggest running the defrag once every two weeks.
Some other people have stated that you should reformat your hard drive and reinstall windows. Well if you do want to go down this path then please, please, please make sure that you back up all your data and files. And you will most likely need the help of at the very least a seriously computer literate friend and I would warn that you may find yourself without a properly working computer for a while. The re-install process is not fast, and you will be amazed what needs updating, how long it takes, and the length of time taken to achieve the level of customisation that you are familiar with now.
You could update your RAM but this needs some serious know-how. You need to find the mother board manual. You then need to ascertain what is the maximum speed of the RAM in Mhz that is supported by your motherboard and possible the processor as well. Also what configuration of RAM chips would be best for the motherboard. And while cheap to buy in most cases, can cause headaches when it comes to fitting so I feel that if you did want to go down this path, then get a professional to do it for you!
So I hope I have managed to offer some help to you Gail, and now I ask for some help. I have only written one long reply like this before and several other posters did, rightly as it turn out, accuse me of coming across as quite big headed. So if you read this Gail, or if you think that the situation that Gail finds herself in is one in which your also find yourself in, let me know how this answer reads. Is it to hard to understand? Do I come across as being to condescending? Or big headed again? I would like to feel more comfortable writing these sort of posts and would appreciate any feedback along those lines.