Normally in a wired network, the computers attach to the LAN portion of the router if it has enough LAN ports that either are on, or can be made to be on, the same LAN; otherwise, an intermediate switch is used. The router manual should be inhaled until it is understood, or at least the relevant parts understood. (My ZyXEL USG 50 tech data comprises about a thousand pages.) Each computer gets an IP address from the router, each of which should be a fixed address (most routers can do this) and then you can communicate from computer to computer using their known respective IP address. File sharing is generally easily done in Linux, but the exact menu path will be different for each flavor.
Wireless setups are similar except all the wires are invisible, and one depends on compatibility between computers and the routers wireless interface.
Otherwise, I think the point of the exercise is for you to learn something, so detailed instructions would be counterproductive, as well as extensive.
Desktop 1: DFI Lanparty UT nF4 SLI-D/AMD Athlon 64 San Diego 2.2 GHz/G.SKILL 1GB x 2 DDR 3200/BFG GeForce 7800 GT/Ubuntu10.04
Desktop 2: Gigabyte 770T-USB3/AMD Phenom II X4 965 3.4 GHz/s. Talent 2GB x 2 DDR3 1333/EVGA GeForce 9800 GT/Mint 14 Cinn-lowlat