The alternator is a bit of a challenge to replace but not hard. It helps to have someone tell you in advance what the pitfalls are.
The alternator ultimately comes out through the passenger lower A arm. You must be a Tetris master to get it to come out. When you get it to come out, remember how you twisted and turned to get it out because you will have to do this in reverse to put it back. This is also a jack stand job, not a wheel ramp job. You want the front suspension at full extension to make room for the alternator to come out.
The AC lines must be loosened all the way across the front rad support and down the passenger side of the engine. Not removed, but all the line retainer clips must be removed.
The wiring is only accessible when the alternator is completely loose from the engine. When the alt is completely detached from the car you can rotate the alt and get access to the wiring.
There is a blind nut or bolt, can't remember which, on top of the alternator. It is a 10MM.
The passenger side engine mount must be loosened to get the long bolt out of the front of the alternator. It is about 1/2 inches too long to get out of the alternator without doing this. Once the engine mount is loosened, jack the engine up high enough that the bolt will clear. We're only talking a half inch or so. When you jack up the engine you can jack it up on the oil pan as it is a solid cast aluminum piece but you will want a piece of 2x4 between the jack and the oil pan to act as a cushion.
It isn't a hard job to do, except you're on your back for the whole thing. I did an alt removal/replacement on my 2003 V8 (your description doesn't say what year you have) in about 2.5 to 3 hours without a manual and with little advice from the board (didn't really ask either) and worked all this out on the fly. Knowing these things, and at the slow rate I work, I could do another one in about an hour.
On the battery, you must get a vented battery. The dealer is the best source for this, and they are actually competitive with aftermarket sources where batteries are concerned.
Finally, don't replace one (battery or alternator) with plans to replace the other one next paycheck. A dead battery cannot be revived, and it will kill a new alternator trying to recharge it. Conversely, replacing the battery but not the alternator would drain the battery to death. However, if you find you MUST do this, replace the battery first. Drive the car as little as possible like only to work and back, and put the car on a battery charger EVERY night until the alternator is replaced.
If anyone sees any pitfalls I missed on the job post it up, the more info Mike has the better.