The Xbox will not work on USB, what model modem is it that you have?
It may also have an ethernet port (which is needed).
You also need a Live subscription starter kit that is available
here for 29.99 or look for offers in your local game shops etc.
You will need to choose a gamertag & variations on it should it be taken (most are) as you cannot change it once selected.
Ideally you may be better off using a router (if you can connect one up) from your modem to connect your PC & Xbox at the same time, to enable them to share the connection. However, initially swapping the network plugs may be your choice (depending upon if you have an RJ45 port on the modem).
Have a look through the posts in this forum & there is much more info available (even an Xbox Live FAQ at the top).