Apple has updated the firmware on the Airport Extreme Base Station so we can use Time Machine now. This is a great thing as now we won't have to remember to pull in the external disk every so often. Though time Machine is smart enough to tell you it has been 10 days or 20 or more days since the last backup.
I will assume you have a Leopard Mac with all the latest updates (10.5.2), an Airport Extreme Base Station (Gigabit Ethernet) also with the latest firmware (7.3.1) and an external USB 2.0 disk at least as big as your internal disk, bigger is better however.
Preparing the Disk
The first thing you need to do is prepare the disk. I'll assume it is a new disk with no files on it. Pull it directly into your computer first and fire up Disk Utility. Select the disk from the left hand pane and in the left pane choose Partition. Select 1 Partition from the Volume Scheme and under Options... choose GUID Partition Table. Press OK. Finally under Volume Information give it a name and most importantly set the format to Mac OS Extended (Journaled).
Click Apply and let it do it's thing. Once it is done you can unmount the disk and plug it into the Base Station. Sadly, we can't do a Time Machine backup and then move it to the AEBS, so we have to do it this way.
Setting Up the AirPort Extreme Base Station
Open up AirPort Utility and click on Manual Setup and select Disks. Go to the File Sharing tab and make sure Enable file sharing is checked. I would also recommend securing your shared disk with a password or some kind.
You won't be able to use that disk for windows file sharing as it is not FAT but, then Time Machine wouldn't work if you did.
Hit Update and wait for your Base Station to restart.
In a Finder window connect to the AirDisk under the Shared items in the sidebar. You may have to login by clicking on Connect As... and entering your password, that may not be obvious but it is an important step.
I would recommend connecting to your AEBS with an ethernet cable for the first backup as Time Machine will be backing up everything and it will take a lot less time over ethernet compared to WiFi.
Open the Time Machine preferences in system preferences and make sure it is on and then select Change Disk and click on the AirDisk. It will start preparing the disk and it will take quite sometime to do the first backup, so it is best to do this before bed so it has plenty of time to do it's thing. It took mine 10 hours to do 150GB, just to give you an idea of how long it will take. After the first one it the hourly ones won't take nearly as long as they are much smaller. You just need to make sure that the AirDisk is mounted.
Moving iTunes Off of Your Computer
You can also use the same technique to move your iTunes library off of your computer and onto a sufficiently large AirDisk.
Making sure you are connected to the AirDisk as above, you can go into iTunes preferences and under Advanced change the iTunes Music folder location to the AirDisk. I would also recommend activating Keep iTunes Music Organized and Copy files to iTunes Music folder when adding to library.
Then actually move all of the tracks you need to go to the Advanced Menu and click on Consolidate Library. This is move all your tracks onto the AirDisk. If you have a big library it will take some time, so hooking up via ethernet is a good idea. You might want to let all this run over the weekend.
If you are away from your network and download more music, video or podcasts, iTunes is smart enough to save them to your local Music folder, to add them to your main library all you need to do is run the Consolidate Library command again.