If you are using Xbox live from Uni or from work you will need to contact your IT department and ask them nicely to open up the following ports.
  1. TCP 80
  2. UDP 88
  3. UDP 3074
  4. TCP 3074
  5. UDP 3330
  6. UDP 53
  7. TCP 53

Those are the ports that the Xbox live service uses which will require opening up on your set-up, without them being opened Xbox Live will not work or you may find you have a strict or moderate NAT. If you have a firewall at home on your router and your Xbox is connected to the router you may also need to open these ports, if you connect your Xbox to the Intenret via your PC you may also need to let these ports through if you have a third party software firewall.

Consult your documentation, a lot of router firewalls will let anything out but not let stuff in so you may find that it will work ok without opening these ports up.

To get info on how to open up ports on your router (known as portforwarding) look here:-

Free Help Forwarding Ports