There are a number of ways to do this...
There are a number of ways you can share files between two people, you can do it through a file server but this isn't always 100% necessary.
First one is e-mailing back and to, as you are currently doing, this is the easiest way of sharing files, it doesn't require you to set anything up and you can just fling stuff back and to all the time at each other but of course you have the problem that every time your business partner wants that file he needs to call you up or e-mail you and ask you for it and then you send it him and that can get a bit of a nightmare.
Another way is to use a system like GoToMyPC, ShowMyPC, LogMeIn or any of the other similarly named applications.
These allow you to create a network connection between your PC and the other persons computer and then the other person can see your PC screen, and any drives you've shared with ShowMyPC.
This again is quite simple, most routers and firewalls are set up to allow these applications through and easily share documents.
The only issue with ShowMyPC is the fact that the other user can also see exactly what you've got on screen and control your computer, there are security checks in place which advise you when this is happening, such as a password and a notification to tell you that the person is looking at your PC (plus also the mouse can start to move on it's own!), but obviously you have to take this into account when using this and ensure that either you can fully trust the person at the other end or you ensure your monitoring what they are doing and protect or hide confidential documents and information you don't want them to see.
Then you can also set up your own FTP server. FileZilla Server will create an FTP server on any Windows based PC (and Linux has it's own version as well).
Using FileZilla Server turns your standard PC into an FTP server (it doesn't require anything like Windows Server or Linux to run, just a standard Windows system works fine).
Filezilla Server works perfectly if both computers are on the same network (on the same router), however if you want to access it through the internet it then gets a little more complicated.
To set up on an local network you just need to install Filezilla Server and then set the directory you want to use as the root and create users and what permissions you give to your users (for example read only, read/write, etc) and whether or not you allow anonymous logging in (normally on a FTP server with private documents on it you wouldn't).
From then on any PC that retrieves it's IP address from the same DHCP server as the computer (DHCP server is normally on the router) can access that computers FTP server by typing into any Windows Explorer window ftp://<ip address or domain name of PC>
To find the IP address of the PC just click start and in the search box type CMD and press enter (on XP click Run... and then type CMD). A black box will appear with all text in it, then just type ipconfig and press enter, a load of text will be on screen and it will amongst that will be ip addresses for your PC normally starting either 192.168.x.x or 10.x.x.x so if your PC has an IP address of 192.168.1.2 then just type ftp://192.168.1.2 and that will access that computer, you can also use the computer name for example if your computer was called maryceleste you could type ftp://maryceleste and then you will see the FTP site.
This of course does all rely on you having the FTP set up on both the router and your PC right, if you find it will only work on the main PC and no others try disabling the firewall for a minute or two and seeing if that makes a difference, if it does then you know the firewall needs to be set up right.
Now as for accessing this method from a computer connected to the outside world - this can be a lot more tricky and is best if you really know what you are doing.
Firstly you need to set your computer up with a static IP address (if your router has DHCP reservation you can use this to reserve a specific IP address for your computer).
Then you need to forward anything going to the FTP port (normally 21) to your computers IP address (using port forwarding options on the router).
Then you need to find out what your routers ip address is for the internet, this is the WAN IP not the LAN IP and whether or not your ISP gives you a static or dynamic IP address. If they give you a static IP that's good, as long as you have all your firewall software set up right and port forwarding set up you should be able to access your FTP site from anywhere in the world just by typing in your routers WAN IP address. If it's dynamic you will need to use a service like DynDNS to turn your dynamic IP address into a static one (or ask your ISP for a static IP address). Then using the IP address they provide you can access your FTP from anywhere in the world.
Another alternative to this is instead of messing around setting your router up and IP address up is to buy some webhosting and use the FTP connection supplied with that as an FTP drive, of course you need to make sure that the folder you create isn't visible to people using http.
There is also cloud based hosting, such as Google documents, this doesn't need much setting up just a google account and then upload all your documents to it. You can then edit your documents through your web browser with Google.
Some other methods that could be used are things like VNC (this shows the PC screen on the other persons computer, like ShowMyPC, but it does need the router setting up the same way FTP server does.)
You could use your own server, but again you would need to set that your router up to forward the ports to it, and the same for a NAS drive.
The simplest method if your not too technical is to use a service like ShowMyPC or LogMeIn, or use Cloud based document hosting as all the set up is already done for you.