Plan on about 2 hours if you are mechanically experienced, or at least 3-4 hours if you tend to drop tools and parts, can't remember where you laid down your tools, like to take pictures so you can figure out how everything goes back together, get hungry, etc. etc.
Two preliminary (optional) steps:
1. Jack up the car and remove the belly pan. Completely optional, but save yourself the trouble and expletives when you drop stuff down through the motor.
2. Unhook the battery cable. Also optional, but probably a good idea since you are working with a part of the electrical system. I didn't do this, but my battery was dead after driving the car home 35 miles with a non-functional alternator. (So dead the window couldn't roll itself up after opening and closing the door.)
Now down to business. Remove the plastic trim on the passenger side.
Now remove the manifold trim.
Take out this black plastic canister thingy.
Remove these clamps and move the hoses out of the way.
Unbolt this metal plate - two 5 mm allen bolts. Be careful when you move it, since there are hoses connected to it underneath. Doesn't need to be completely removed, just loose so it can be moved around. You'll want to disconnect the hose on the left side (passenger side) of the plate.
Using a 15 mm open end wrench, pull the belt tensioner toward you to slacken the belt. (Can't really tell in this picture, but that's what I'm doing here - wrench is in my hand.)
If you pull the tensioner far enough toward you, there are two holes that line up and let you slide something through to hold it in place. (You actually have to get it this far to get the top alternator bolt out.) I used a nail.
Now remove the belt. But before you do, somehow mark it so you know which direction it was going. It needs to go back on the same way it came off (according the Bentley manual). I used a piece of duct tape.
Remove the top alternator bolt. 13 mm.
Remove the bottom bolt. 13 mm again. I used a u-joint on an extension.
Remove the wires. One is a socket that unclips, the other is bolted on (I think a 13 mm, can't remember) covered with a plastic nut cover (that pulls off). That same wire is also held on by a clamp at the bottom of the alternator (8 mm nut). That clamp is easier to get to once the alternator is loose from the bracket.
Now for the tough part. There are bushings that hold the alternator to its bracket - tightly. It won't budge. First thing to do is spray some penetrant (PB Blaster is what I used) on the bracket where the alternator attaches. Let it soak; spray some more if you want. Then do whatever you can to get it to move. I whacked it with a scrap of wood and hammer. Be careful doing this - try not to rest the block of wood on the splines, since they will break off! (I really didn't care so much, since the alternator was dead anyway.)
Eventually, it will start budging, a little at a time. You just have to get it past its bushings and it will free up. Now remove the wire clamp from the bottom of the alternator. Then work the alternator up out of the engine bay, towards the passenger side, clearing all the hoses. (It won't fit up through the manifold side).
On the replacement, you have to edge the bushings out a little to give clearance to get it into the bracket. I shot them with penetrant, inserted one of the bolts, threaded a few turns, and rapped on it with a hammer until it moved a bit. You only need a millimeter or two of clearance, so don't go crazy with the hammer.
Work it back into the engine bay the same way the original came out. Before you bolt it back into the bracket, attach the wires and the cable clamp to the bottom with the 8 mm nut.
Don't forget the plastic nut cover.
Now start reattaching everything. Put the belt back on (noting the direction you marked earlier), remove the nail from the tensioner, hook all your hoses back up, reinstall the canister, replace your covers, and start it (or, in my case, jump start). That's it.
I picked up a salvaged alternator on eBay from a '00 parts car for $85. My car has over 132,000 miles on it so I didn't feel like investing $250 plus the core for a rebuilt model. But so far, it's running great! Here's the voltage display on the Passport 8500 a minute or two after starting - charging away. It eventually settled down to about 12.8-13.0 V (with the lights on -- little higher with them off).