At the time of writing, Apple have three distinct AirPort models: the AirPort Extreme, the AirPort Express & the Time Capsule - this guide addresses only how to set up internet connectivity for wireless clients through the base station so in this respect the following information should be generic across the product line up.
Note that, although a base station has many possible configurations, you are strongly advised to adhere to the advice outlined so as not to interfere with existing network services. If you have queries then please get in touch with ISS Help Desk.
Open the AirPort Utility and connect to your AirPort - the utility should find the base station automatically for you.
Click the Manual Setup button.
Select the Base Station tab & set a name and an administration password plus set the time to auto-sync with Newcastle's time server ntp0.ncl.ac.uk

Give the Wireless Network a name & a channel frequency (you can use Automatic in most cases). If there are multiple base stations in the same building then it's preferable to select a different channel - in the event of a conflict with channel 1, channels 11 or 6 should be tried.
You should use "WPA/WPA2 Personal" encryption as this provides the strongest encryption for data passed to the base station plus allows the most compatibility with Wi-Fi enabled devices.

Register the hardware address of the base station's Ethernet port (this is the WAN port in the case of the Extreme or Time Capsule) so that it can pick up its IP address automatically using DHCP.
It is important that the Connection Sharing setting is set to Off (Bridge Mode) so that you don't interfere with existing DHCP servers on the campus network.
You should also take the opportunity to add the AirPort ID of each AirPort enabled client into the base station's access control list to allow only these registered clients to use the wireless network provided by the base station.

Finally you will need to register each client's AirPort ID with ISS. This may mean that the same computer has been registered twice (once for Ethernet and once for wireless networking). You will need to register distinct names in each case and you will receive a separate IP address for each.
Clients should have their AirPort network port in their Network system preferences set to obtain an IP address Using DHCP as shown here:

Also set the both Web & Secure Web proxies to wwwcache.ncl.ac.uk port 8080

and the SOCKS proxy to socks.ncl.ac.uk port 1080

You should now be up & running!