Connecting the computer through a crossover cable, you'll have to set up Internet Connection Sharing, but if you have a router, that's really not the best way to do what your trying to do.
My suggestion would be to get rid of the crossover cable, and connect the second PC to the router with a lenght of CAT5 cable. Then just set both PC's to obtain IP addresses automatically. This way you don't have to have PC #1 on for PC #2 to get online.
Then just go to your printer properties, enable sharing, then go to add printers wizard on the other PC, map it, and you should be all set.
Project time 1/2 hour, difficulty level very simple