gassoncp, you don't HAVE to have wireless and if your second computer is downstairs it may not be the best option. How you connect your computers is a matter of balancing needs convenience and cost.
To build a network you will need a modem, a router, and a switch plus some way to connect the computers to each other. For this you can use network cables, household wiring or wireless.
Your existing modem may well have modem/router/switch combined - it may also have wireless. For these the modem manages your adsl connection, the router handles network trafiic, and the network switch manages the network connections. If you're not sure what you modem has then check the manual or ask the supplier. If your modem doesn't have these then a new adsl modem with all combined will generally cost from around £40 upwards. With a combined setup (it's unlikely you'll get them seperately) then all you need to do is connect you computers to the modem and configure.
To connect the computers you'll need network cables ("Cat5" ethernet), "homeplug" or wireless (802.11 b/g).
Wireless has some issues. It will require more configuration to ensure it is secure. If you do want a wireless network then do be aware that it is very possible it won't give you the coverage or performance you might hope for or expect. You may have to guddle about with the location of your wireless kit (including the PC) to get a decent connection. For this reason you may need to consider consider placing wireless near where you need it rather than just where it is convenient - and so end up running cables to position it! Connectivity can be problematic especially between floors and especially if you live in an old brick or stone built house. I would not recommend it blindly as your first option, and it is certainly not compulsory. If you do have an old house then MIMO (pre-N) wireless hardware reports much better coverage though I've not used it.
Ethernet cables are easily the best option for security and performance but clearly laying them round the house can be a pain. Despite this cabling is in many ways the simplest option - just plug your computers into the switch, set up the computers (Micro$oft have wizards and a good help section to do this) and that's you done. I think cables are about £1-2 per metre.
Another option is "homeplug" - ethernet over the household mains. You will need one homeplug adapter for each access point - so a minimum of two (one at each end) to create a network. A set of two homeplug adpaters will cost from around £50 upwards depending on the spec. Don't mix and match "homeplug" with "homeplug AV" because they won't work together.
Finally, search the web for advice and the best prices.
Hope this helps!
