Pretty much any modern day router will do. You plug the part that goes into your computer into the router, and then you can plug another networking cable from your computer into the router (there will be a few ports for hardwired connections.) Follow the install instructions that come with the router. Be sure to password protect it if it isn't by default. Also, I would recommend renaming the router if it comes with a generic name like "LINK382" because there will end up being a "LINK812", "LINK408", and "LINK772" in your area and you will have to spend brain cells memorizing which one is yours.
As far as technical specs, the routers are usually differentiated by a letter after the 802.11 code. A & B are really old and you would expect to see them in a garage sale somewhere. G is the primary technology in use now, but N is definitely newer and faster and should be what you go for if you are buying something new. If your neighbor has an old G router, but doesn't need it anymore, you certainly can use that instead.
Just looking super quick, here's a 802.11n for $30 from TRENDnet:
http://www.tigerdirect.com/applications ... CatId=2668D-Link for $40: tigerdirect dot com/applications/SearchTools/item-details.asp?EdpNo=5650958&CatId=2668