How can I take apart this leaking outdoor faucet?
That nut should turn, but hit it with some penetrating oil (WD-40) first and let that soak in. Try to use a wrench or socket if you have one that fits snug, rather than pliers, since pliers can damage that nut. Finally, be careful when rethreading the nut back on since it's easy to cross thread or strip the threads.

If the plumber that installed this was nice, you may find the entire faucet is attached via a threaded pipe and can be spun off. My plumber was less kind and soldered the threads, so I'd have to open the wall and replace the pipe to change out the faucet. Keep in mind that when a faucet like this gets old, it may not be good enough to change the washers and repack the stem, so keep your option to replace the entire thing open.