Terry's almost right. Assuming you already have a cable/dsl connection into your desktop then you will need to buy a wireless router.

Many routers (i.e., linksys, etc) have 3-4 hard wired ethernet ports, and the wireless access. So if your existing computer already uses an ethernet connection (as opposed to a USB connection to the broadband modem) then there is nothing further to buy for the first computer - otherwise you will need to buy a NIC (network interface card) either wired (about $10) or wireless ($20-50 depending)

The second computer will require a wireless card so it can exist and connect to the router.

There are 3 "standards" for wireless - 802.11a/b/g. You can get a router that does all three (although very few people use "A") and if you get a "g" it is backward compatible - just make sure whatever you get for the router, you are getting the same for the NIC card. "G" gives you the longest distance and highest data rates (similar to cordless phones, higher Mhz/Ghz for longer distance).

You should be able to purchase a decent "G" broadband router for about $80 with a card for about $40-50 from your local best buy, compusa, etc.