A router makes one external connection to the internet and shares it between computers connected to it, so your ISP thinks there is only one device connected. You will have heard of a hub, which is just a type of junction box connecting computers together to form a network? This sends all the network traffic down all of the lines at the same time. A switch is an intelligent hub that remembers where each device is and only sends the relevant traffic down each line. Sooo.... a router is a switch with a modem built in. Either use the switch to make the network and use internet connection sharing from one computer on the network, or use the router to make the connection (the Gateway) and each computer connects through it. PHEW! Hope that makes sense. You don't say how many computers, what OS's and how well you understand configuring networks, which all affect the choice of solution.
well i am connecting 2 pcs running winxp pro on one and win me on another. Thanks guys, i have now cancelled that other modem, i was scaredd it wouldnt work well and am now ordering a much better one. thanks all for advice and help.
sorry, took so long to type my reply missed bremners posting. Sorry, bremner, but if there's only one connection with three computers, they each can only have a third of the bandwidth irrespective of the connection method if all connect at the same time. The difference is that arouter is more efficient at sharing the available bandwidth and so will run slightly faster. On a home network you are extremely unlikely to see any difference, but on a commercial network of twenty or thirty that would be a big difference.