The following is the best way.
Cable Jack on Wall
(hmm, dang post won't keep the multiple spaces I put into the diagram)
Why are you using a USB network adapter? Doesn't your PC have an ethernet jack? Usually the jack is builtin to the motherboard (close by the USB/Keyboard jacks) or has an expansion card version. USB ethernet tends to lag badly.
Do you have a home router? If not, you're playing a dangerous game with hackers being able to easily gain access to your network. Windows' Firewall isn't good enough to protect you.
Are you planning on using the 360's builtin ethernet jack or are you thinking of going wireless in the future (even though not right now)? If wireless in the future, get a router with both 4 ethernet ports and WiFi.
Not knowing what you have, I suggest you go to the local store and get a Linksys WRT54G router (course others will suggest whatever they've used, I have had to deal with all brands). Then connect as the diagram above shows.
I don't like "going through" a Windows PC for shared Internet. Yes it can be done by using ICS (Internet Connection Sharing) but then yor PC has to be on all the time, it's a bottle neck for the other PC, etc.
Also, if you want to do the ICS router, your PC must have TWO network adapters. You have one (your USB dongle) so you'll either need to find out if your PC already has an ethernet port or go buy another USB version or a card version.
If you get a wireless router, make sure you disable the WiFi until you're going to use it.