Answer Best answer as chosen by user ilo_v
What is a router?
Hi, let's try and sort this out for you. Simply, a router is designed to route a digital signal to one or more connected devices. There are various types of routers, with different characteristics and uses.
I'm not quite sure what you mean by your "Motorolo thingy", so I'll just limit my comments to your laptop internet connection. Also, I should point out that I'm not in America, so I don't know exactly what AT&T supplies but I'm going to assume it's the same as DSL/ADSL connections in the rest of the world. I'll start by assuming your telephone line is copper, not fibre optical (we'll note the differences along the way).
On copper, the phone company supplies voice and data on the same physical line. at the point it enters your house, the first thing needed is a filter to separate the voice from the data. Usually, this is a small box with a single RJ11 or RJ12 socket on the input side and two such sockets on the output side, one for data and one for voice. The line into your house plugs into the input side and your regular house phone plugs directly into the voice socket on the output side. The DSL modem plugs into the data socket on the output side. Usually, all these cables are thin grey 2 or 4 wire. The output side of your DSL modem will have an RJ45 socket (wider, usually coloured yellow). You then plug a CAT5 or CAT6 Ethernet cable into the output side of the modem and the other end into the device you want to connect to the internet, in your case, currently, your laptop. Conventionally, this cable is yellow and contains 4 twisted pairs of wires to connect the modem to the laptop.
Some phone carriers combine the splitter and the modem, so that you have just one box, with a single RJ11 or RJ12 socket on the input side. connected to the incoming phone line and on the output side, one RJ11 or RJ12 socket, into which you plug your house phone and one RJ45 Ethernet connection into which you plug the yellow Cat5/6 cable to your laptop.
If you have a fibre optic connection from the phone company, the voice and data signals are provided on separate fibres and so you do not need the filter. The wall socket will have two connections, one RJ11 or RJ12 for the house phone and one RJ45 socket for the modem.
OK, one of these schemes will apply to what you have already. If you want to connect more than one PC you would use a router to do it, essentially setting up a home network. The router contains a DHCP server which will assign a separate Internet Protocol (IP) address to each computer on your internal home network. It will use these IP addresses to separate the signals for each of the connected computers and route data between them. It will also use a function called Network Address Translation (NAT) to translate your internal IP addresses to the external IP address your phone company supplies. This enables multiple internal network computers to share the single Internet line supplied by the phone company. Most routers also contain a hardware firewall, which provides your internal home network with an additional layer of protection against viruses and malware. To perform these functions, the router can either be wired (all computers are tied into the router by RJ45 Ethernet cables) or wireless, where the cable is replaced with a wireless signal. Note that all wireless routers also have at least one and usually more wired connections to allow you to configure the wireless network. Each computer connected wirelessly will require a Network Interface Card (NIC) to "connect" to the wireless network. Most laptops have had a NIC built in for several years but if you have an older laptop that doesn't, you can add one, either via a USB dongle or a PCMCIA card.
One other variant here, sometimes, the modem and the router are combined into a single unit, imaginatively called a "Modem Router" or sometimes a Gateway. Some phone companies supply such Gateways in place of the modem, usually for an additional charge.
Wireless routers come in different speeds. designated by a letter after the protocol (802.11). The designations are "A" short distance high speed, "B" short distance (but longer than A) low speed (11 Megabits per second (Mbps), "G" medium distance medium speed (54 Mbps), N long distance high speed (150 Mbps). There are also N variants, N300 (300 Mbps), N600 (600 Mbps) and N900 (900 Mbps). You are unlikely to find any of the older A or B routers nowadays and Gs are being phased out. So I'd recommend you go for an N and as you appear to have only one connected machine at present, a straight N (150 Mbps) should suffice. It SHOULD be faster than the speed AT&T are supplying to you and should match the NICs in your attached machines. Within the internal different speed router and NICs can coexist and will establish the appropriate connection speed at sign on.
SO looking at what you asked in your question, if you want to untether your laptop, you need to ensure it has a NIC installed (check in device managed, Network Adapters) or get a USB dongle or PCMCIA card, get a wireless router, unplug the yellow cable from your laptop and plug it into the modem port on the router (this is also usually coloured yellow), ensure the NIC is enabled and follow the installation instructions in the router manual (you may need to plug your laptop into one of the router's wired ports for the installation, for which you will need another RJ45 cable). You can now wander all over your house with your laptop! Always assuming it isn't a steel framed house, of course, wireless signals are shielded by metal!
Most routers are supplied set up to enable an easy first connection, which should include a minimum security set up but once your network is working, you will need to customize your settings through the router's control panel (usually accessed from your browser). I would suggest that you should change the SSID (the name of your network) and stop broadcasting it (you then need to check the box in your NIC setup on the laptop to say connect even if the network isn't broadcasting), change the password on the router control panel, set up MAC control so that the router will only respond to the MAC address on the NIC cards in your network and not some passing stranger, and MOST IMPORTANT, configure the security setting to WPA2-PSK with a strong passphrase. Your router manual will explain all this Note that your NIC settings must match your router settings.
It might sound a bit complicated but it is straightforward as you work your way through it.
Hope that helps, good luck!