This can be either very easy or very difficult depending on who your isp is. There is a way to connect using ICS (internet connection sharing) but it is pretty complicated and I've never needed to do it myself. You can get a how to on that from
www.xbox.com. If you used ICS that would mean you wouldn't need to swap cables.
Best and easiest way is to simply plug in your ethernet cable into the xbox from the modem. Once plugged up, turn on your xbox and click on the
XBOX LIVE tab then click
JOIN XBOX LIVE. Enter the relevant details it asks you like voucher number, credit/debit card number if asked. If it won't let you connect you will need to go into the
SYSTEM tab and find
NETWORK SETTINGS. Click
TEST XBOX LIVE CONNECTION and it will run a series of tests like network adaptor, ip address, dns, etc. If it finds these without a problem you should be in business and go back to the
XBOX LIVE/JOIN XBOX LIVE tabs to enter your details.
If it doesn't you'll need to set it up manually. To do this you will need to know your ip address, gateway address and the dns server address (usually the same as the gateway). If you don't know these you can find them in windows. You'll need to plug your pc back into the modem and be connected to the internet. If using XP click the
START MENU and then click on
RUN. If you are using vista click the
START MENU/ALL PROGRAMS/ACCESSORIES then
RUN. It will bring up a small box. Type in
CMD and hit return. Another box should appear with a black background. It should say documents and settings - type in
IPCONFIG/ALL and hit return. A list of details should appear. Search down to find your ip address and gateway - it should start with either 192.168.*.* or 10.0.0.*. Write the details on a piece of paper and plug the xbox back into the modem.
Now go to the
SYSTEM tab and find
NETWORK SETTINGS/EDIT SETTINGS and enter your ip address and gateway into the appropriate boxes manually. Run the
TEST XBOX LIVE CONNECTION and see if all is well. If so go back to the
XBOX LIVE tab in your dashboard and click join xbox live and enter the appropriate details.
With any luck you should be now connected to xbox live. It might be worth buying a cheap ethernet modem from ebay with more than one plug at the back so you don't need to swap cables all the time.

Good luck...