Using Time Machine with an Airport Extreme AirDisk
Q2. How do I set up Time Machine to back up to an AirDisk on my Airport Extreme?
You can use a single self-powered USB drive with an Airport Extreme, but if you want to use multiple devices, or a disk that doesn’t supply its own power, you must use a powered USB hub. See this Apple Support article: Uses for the USB port of Time Capsule, AirPort Extreme, AirPort Express.
First, set up your Airport via Airport Utility (but don't connect the drive to it yet), using the instructions that came with it. If you can’t find them, see:
Airport Extreme Setup Guide (tall, 2013 "ac" model- 6th generation)
AirPort Extreme Setup Guide (early 2009) not supported
AirPort Extreme Setup Guide (802.11n) not supported
AirPort Extreme Setup Guide (Gigabit) not supported
Keep the name you assign to it, your Computer, and your network short (under 25 characters), and avoid embedded spaces, special characters, and punctuation. Connect your Mac to it. (See problem #P1 for details.) Make sure it will work via an Ethernet cable if at all possible, in addition to wirelessly.
Next, attach the drive directly to your Mac, and erase and format it per the instructions in Time Machine FAQ #5. Note, however, that it doesn't matter whether you use the Mac OS Extended (Journaled) or Mac OS Extended (Case-sensitive, journaled) Format for the Time Machine partition, since Time Machine will put your backups in a case-sensitive sparse bundle. (You can use the procedure in item #A8 to change that if desired, by cancelling the first backup as soon as the sparse bundle is created. See the discussion in the pink box of Time Machine FAQ #5).
For other partitions, of course, the Format is important.
If you're backing-up multiple Macs to the same drive, you can make one partition for each, but it's not as helpful on a network drive, because each Mac's backups will be in a separate sparse bundle. So you can let them share the entire disk or a partition if you prefer.
Steps a. and b. below may not be necessary on the new, tall Airport Extreme.
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a.Your Airport shouldappear in the Shared section of your Finder sidebar. If it doesn't, select Finder > Preferences > Sidebar from the menubar. Be sure the little box for Connected Servers (or Bonjour Computers) is checked. Click your Airport name in the sidebar.
If you don't use the Finder this way, click on your desktop so you get a Finder menubar, then click Go > Connect to Server, then the Browse button. That should bring up a Finder window listing your Airport; double-click it to open it.
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The sample is shown in column mode: from the menubar, select View > as Columns.
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b.Either way, you should now have a Finder window listing the partition(s) on the USB disk. Double-click the one you want to use. You should see a "connecting to server" message briefly, then an empty Finder window for the partition.
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c.If the Time Machine icon isn't already in your Dock, drag it there from your Applications folder (see Time Machine FAQ #24 for information about it).
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d.Control-click (right-click) it and select Open Time Machine Preferences, click the Show Time Machine status in the menu bar box (see Time Machine FAQ #24), then click Select Disk (on Leopard, this button will be either Choose Backup Disk or Change Disk).
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e.A list of possible destinations will appear It should include the USB drive/partition you clicked in (b), and may show other internal or external drives/partitions as well.
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Select the USB partition and click the Use for Backup button.
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f.A prompt for your name and password will appear. If the name isn't already filled-in, enter your short user name. Also enter the password you set up for the Airport via Airport Utility, then click the Connect button.
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g.A 120-second countdown to the start of the first backup will start in the Next Backup area of the TM Preference panel.
Effective with Mountain Lion 10.8.x, you can specify two or more destinations, and have Time Machine back up to them alternately. See Time Machine FAQ #34 for details.
Note that the first backup will copy the entire contents of your system, except for a few things that are skipped automatically, such as system work files, most caches, your logs, trash, etc., and anything else you may have excluded (see Time Machine FAQ #10 and #11. So it will be rather lengthy, depending on how much data is on your system, whether you're connected via Ethernet or WIFI, and if WIFI, how good the signal is.
You can continue to use your Mac while TM is backing-up, and you can even cancel a backup if necessary, but to make the first full backup as fast as possible, try not to overload your Mac or cancel the backup.
Speeding up the first full backup:
Once this is all set up, and the first backup has begun, there is a way to speed it up:
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•As soon as the sparse bundle has been created, cancel the backup (click the small circle with an "X" at the right of the progress bar).
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•Disconnect all users via Airport Utility > Disks (if you have Airport Utility 6.x, there isn't a Disconnect All Users button. Download and install Airport Utility 5.6 (you can have both at once, but it won’t install on Mountain Lion. You can download Airport Utility 5.6, then use the Pacifist app to extract it). Then disconnect the drive and connect it directly to your Mac.
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•Re-select the (now local) disk via Time Machine Preferences.
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•Select Back Up Now from the Time Machine icon in your menubar.
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•When the backup is done, you won't see it normally via the Star Wars display while the drive is connected directly. Double-click the sparse bundle via the Finder to mount the disk image, then double-click that to mount it, then Enter Time Machine.
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•Eject and disconnect the drive and reconnect it to the Airport Extreme. Re-select it via Time Machine Preferences. Time Machine should display it normally.
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•Regular, hourly, incremental backups will continue wirelessly.
If you need to do a full system restore:
Eject and disconnect the drive, connect it to the Mac to be restored, and see Time Machine FAQ #14.
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Note that if you've been doing backups to an external disk connected directly to your Mac, you cannot continue the same set of backups when you connect it to your Airport. They are stored differently, and Time Machine will put the new ones in a sparse bundle, alongside but completely separate from the backups made locally, and the first backup will be a full backup of your entire system. You may be able to copy them to accomplish this, though, per Time Machine FAQ #18.
Once the USB drive is set up the way you want it, connect it to the Airport. Now you're ready to configure Time Machine:
The setup and first backup (of your entire system) will be much faster if you connect via Ethernet.
By default, Time Machine will back up your internal HD. If you have multiple internal HDs, and/or multiple partitions, they'll all be backed-up. If you don't want some of those backed-up, you can exclude them, per question #10.
If you want to back up one or more external HDs/partitions, you'll have to remove them from the exclusion list, per question #10. Also see question #32 for info on backing-up multiple disks/partitions.
If you're backing-up more than one Mac, see question #33.
Time Machine can back up to a USB drive 
connected to the new, tall Airport Extreme "ac" models (6th generation) introduced in June, 2013.
But it's not reliable and not supported by Apple on the older, flat models. They have different hardware. If there's trouble with it, you won't get much, if any, help from Apple. If you decide to take the risk, you'd be well advised to have other backups; don't depend on these 100%. See Time Machine FAQ #2 for supported Time Machine destinations.