Okay! It's kinda long and involved, though... without further ado...
First of all, don't buy a new one until you have the old one tested to make sure its bad. You DO have to take it out to get it tested, but anyway... take it to Advance Auto Parts to have it tested. Autozone didn't have the right equipment to test mine. But I did buy my replacement alt from Autozone for $169, and it's still doing great.
To get it off:
Unhook the battery.
Jack up the front as far as you safely can.
Take loose the Y-pipe at the catalytic converter (probably 3 bolts, maybe 2. These bolts are usually rusted and frozen in place, so they take a lot of WD-40 and a lot of beating).
Take loose the Y-pipe at the rear exhaust manifold (2 bolts).
Take loose the hanger in the Y of the Y-pipe that holds it up to your engine (1 bolt).
Unplug both bottom oxygen sensors- one on the Y-pipe, and one on the front manifold.
Take loose the Y-pipe from the front exhaust manifold (2 bolts), and it will drop right out of there.
Now you can see the alternator. Its on the back of the engine, right next to the rear exhaust manifold.
Remove the serpentine belt by sticking a 3/8" drive breaker bar into the slot on the front of the tensioner pulley and prying it away.
The alt has 3 electrical connections to unhook. One just unplugs, one is a plug held in place by a metal clip, and the big one is held on by a bolt. Take all these off.
There is a little bracket on the back of the alt, holding it against the block. One bolt is in the alt, and the other is in the block. They both have to come out (I think they are 10mm, and you will need a u-joint and an extension or 2 on your socket).
All that remains now is the 2 big bolts that hold the alternator onto the block. They are, I think, 15mm. You will need one deep-well socket, one u-joint, and about 18 inches of extensions. The bottom bolt is pretty easy to get to. The top is not. Take the bottom bolt out and take a break.
To get the top bolt out:
Remove the front passenger's side wheel.
Remove the black plastic splash guard behind it- the smaller one at the bottom of the fenderwell, not the full piece.
Take the tie rod loose from the hub. You may need to rent a tool for taking the tie rod end out- some are really sticky, and they get deformed if you have to beat on them.
Now you can see the alternator from here.
Reach in through the fenderwell, and try to feel the top bolt. It's easier than sticking your hand up from the bottom of the car. When you figure out where it is, take your deepwell socket ONLY and attempt to put it on the bolt from there.
Once it's on the bolt, go back under the car with the U-joint and the 18"-odd-inches of extensions. You should be able to see the socket you just put on, and it shouldn't be TOO hard to snap the u-joint onto it from down below. Then you can remove the top bolt.
Now your alternator is loose. Wiggle it out of the bracket, and go back to the fenderwell. You have to pull it out through there. It takes a lot of twisting and moving around- it's kinda like a puzzle, trying to figure out how this thing needs to twist to fit out through the little hole. But it will.
And that's removal. Re-installation is just the opposite.