How do I connect my xbox 360 to the internet?

You are right if you do not want to do any cabling you will need two devices: a router that supports wireless and a wireless card for the xbox.

There are a number of wireless routers: linksys, netgear, d-link, etc. All good components. All have basic features that allow interbrand operability and most of the big companies have proprietary features (like speedboosting, etc) that are specific to their brand.

I happen to have a Linksys WRT54G which is a fine wireless router and would accomplish exactly what you desire. It is very easy to setup if you will read the directions and patiently perform them exactly as each step describes.

The wireless router that you choose will go in between the cable modem and your PC adding a second layer of security for your PC and home network. Be sure not to skip the encryption steps, as this will prevent unauthorized people from using your internet connection. This also means that you can let friends/relatives easily access your internet connection with their wireless enabled devices like laptops, Nintendo DS’s and iPones etc.

The wireless card for the xbox will easily attach to your wireless network once it is setup and away you will go.

Hope this helps.

While I probably will not get too many points for simply referring you to another post, check out this question I asked a couple months ago and got great responses to:
http://fluther.com/disc/3354/how-do-i-set-up-my-xbox-360-to-the-internet

Also, as I ended up hardwiring to the adjacent wall jack, I did not end up using my wireless antenna for the Xbox 360; I still have this device and would be willing to sell it at a significant discount if you end up going ahead with this. Not mean to be a solicitation, but an offer to help you get this going at a discount!