You can't just connect both computers together, you need a "Router" - there are different types available at reasonable cost, including "Wireless" ones.
You didn't say if you have a dial up modem connection or are on Broadband.
For example if you have a stand alone modem, as opposed to a modem installed in one of the computers, then you would connect the Modem to the Router.
Each PC will need a "Network Card" installed in it ( These are also available as Wireless if you are gong to get a wireless router ) and this is used to make the connection from the PC to the Router, and thus share the Internet connection.
There are also combined modem / routers available.
Once the Network is set up in this was you can go on to "Share" files between the two computers and / or Share a Printer attached to one of them.
This should get you on your way - to look at the types of Router and Network cards available have a browse around o eBuyer.com click here or Dabs. com click here
Good luck !
"Boot-It-Out" click here