Ok before i start ther is no point in reading this if:
1)you havent got wireless
2)you do not have a wirless enabled computer/laptop within ethernet cable range of your 360.
Ok then to hopefully save your monies here goes.
plug in your xbox to you computer via ethernet
(control panel>network connections)
open up your "network connections" window and see if you can see your xbox's connection.
(if not check you have ethernet drivers installed for your computer)
right click your internet connection,click the "advanced" tab,click allow other users to connect...",click apply
right click your xbox connection,click internet protocol,click properties
change the ip to: 192.168.0.99
change the default gateway to:255.255.255.0
check your routers dns, it needs to be 192.168.1.1 (i dont know fully how to check this but heres one basic way. try typing 192.168.1.1 into your browser. if it comes up with anything then thats your dns. also belkin are normally 192.168.2.1,netgear 192.168.0.1, just google how to change it)
anyway put you primary and secondary dns to 192.168.1.1
click apply and exit
turn on your xbox and goto network settings
change the ip to :192.168.0.99
default gateway to : 255.255.255.0
change dns primary and secondary to :192.168.1.1
test xbox live and if all went well you can connect!
you could always buy one of the following used linksys router models off of ebay
Flash the linksys router with 3rd party firmware then set it up to work as a client or wireless bridge. You would then put the router next to the Xbox360 and run a short ethernet cable from the 360 to the router. This would also allow you the ability to network other components near that router.
That would probably only cost you $20-40
You could also look into the following Buffalo routers and do the same thing. They sell between $35-50 new usually.
That's a lot cheaper than paying $100+ for Microsoft's accessory and it would achieve the same result of allowing you to have wireless access from one part of your house to another part of the house where your cable/dsl modem and main wireless router are situated.