Assuming that your internet connection is broadband, then to keep it simple, both PCs will either need USB (for wireless) or a network connection port for wired.
Then you'll need a Wireless ADSL (i.e. broadband) Modem Router plus a USB wireless adapter for each PC that you wish to connect wirelessly and a network cable for each one that is to be wired (it is always recommended that at least one is wired).
Then the Router connects to the internet and both PCs connect to the router (as a network hub). Then each PC can access both the internet and the other PC via the Router.
Ebuyer has a fair selection of kit (click here). But make sure what you buy is a Wireless ADSL Modem Router. You'll also find packages that include a USB wireless adapter with the Router.