While a full explanation of computer networking is outside the scope of this forum, generally, you either want to have two computers connected directly together by a crossover cable (so, 2 computers and 1 cable) or, preferably, have each computer connected to a hub via a normal cable (so, 2 computers, 1 hub, 2 cables).

If you can look at the connector on your current cable, you can usually determine what type of cable it is. Hold it flat so that you're looking at the clip side. Look at the first three wires on the left and the sixth wire. Determine what the colors are (keep in mind that some of the wires will be solid colored and some will be striped, usually with white). Then fingure out the colors of the wires in the connector on the other end of the cable in the same way. If they match up, then it's a normal cable. If wires 1 and 2 on one end are wires 3 and 6 on the other end, and vice versa, then you have a crossover cable. The other four wires are unused in most ethernet applications, and, therefore, irrelevant.

Of course, setting up actual networking once you have the cables proper is non-trivial as well. Try reading the FAQ entry about ethernet. It should give you some ideas.