Hola
JamesT and welcome to the board
There are a few routes you could go here. One of the more popular ways is to setup a router for both systems to share. Your adsl modem connects to the wan (wide area network) port of the router and your systems connect to the lan (local area network) ports. Most routers should automatically assign local ip addresses for your systems and allow both online together. The other big choice would be if you'd like a wireless connection or not. This is handy with a laptop, but not necessarily needed on the desktop system. I'm sure others will chime in here as to what their brand preferances are. I currently use a linksys 4 port and have 4 systems connected to it
Hope this helps
~Peace
DC