Thanks in advance.
Answer:
You can go about in 2 different ways:
1) You buy a wireless router: But this option is not going to be too reliable since from my understanding the xbox and the computer are going to be quite far from each other. For xbox live, you need to have full strength wireless connection. Not only that, you'll have to end up buying a wireless network adapter for the xbox which will cost you another 50-80 bucks depending on whether you buy the original adapter from microsoft or a third party one. So this option is not only going to be too costly, but also not totally reliable
2) You could go with a simple router(doesnt need to be wireless) which will be a lot cheaper, and buy 2 long ethernet cables that are long enough to go from the router to the xbox and another one going from the router to the computer. Because they are cable connections, they will also be 100% reliable.
The only problem is the ethernet cables dont come too cheap either, especially the long ones. But if you go to THE SOURCE (canada) or TIGERDIRECT (USA), you'll find good deals there.
Personally, i would go with option B but some hate the hassles that come with wires, and so go with option 1.
P.S: Whichever option you go with, you can get technical support from microsoft 1800MYXBOX. Not sure about the number but they do help with connections. Make sure you have the stuff u need before you call them so they can better assist you.
Hope this helps 
{ 4 comments… read them below or add one }
I'd suggest a Cisco/Linksys.
You may want to move the modem upstairs near the Xbox and use the computers internet Wireless, because it is a lot easier to get a wireless card for your computer (it may already have one) than to get a wireless thing (its not a wireless card so i don't know what to call it) for your Xbox.
As to setting up your router when you buy it it will come with instructions and a CD (At least if its a cisco/Linksys it will, i don't know about others), just follow the instructions.
Get a wireless router, any model will do. I used to have a wired router and had to run an ethernet cable downstairs to my xbox, it was a pain in the ***.
router and long cable = ~$50
or
Wireless router and xbox wireless adapter = ~$170
In addition to a wifi router you would also need a wireless card for ur 360, or a fn long ethernet cord. Wireless routers are fairly cheap, u can find them for like $30 (practicably any model will work) , with it u can connect both ur 360 and ur desktop. the wifi adapter for the 360 though will set u back 80 big ones. Im not sure how much the ethernet cable would be (depends on how long u need it), but i assume it would be cheaper although more cumbersome than the the wifi adapter. If u happen to have a laptop with wifi also, u could connect ur xbox directly to that with a crossover cable(ten bucks at radio shack, looks like ethernet cable). once the laptop is connected to the 360 u could bridge the 360 connection to the wifi one, this connects ur 360 through the laptops wifi. The bridge would be cheaper if u have a laptop, but it might slow u down a little. good luck.