Standard 10baseT patch cables have the same wiring arrangement at both ends. One uses these patch cables to connect each PC to a hub.
If you have only two PCs to connect, you do not need a hub. You can make a special crossover cable, that connects the two PCs directly.
The wiring diagram of standard connectors and crossover connectors can be found at http://ourworld.compuserve.com/homepages/J_Helmig/thisted.htm and http://speedy.fsn.net/10BaseT.htm.
Note that the pairing is important. White/orange and orange/white wires are twisted together to form a pair, as are white/green and green/white. Color is not important, but pairing is. If you do not have a proper wire pair on pins 1 and 2, for example, then your cable will not work.