I have the same problem with 2.0L. 16V showing. Battery was smoking. I will ask the same question...looks pretty simple but is there a step by step or walk through for alternator replacement? Also would you recommend replacing the thermostat while the alternator is out just because it is easy to get to? I don't know the age of the thermostat.
Not sure if this is still relevant to you or not, but here's a basic step by step that I did for my alternator swap. Second time took me 45 minutes and that's including the run to the parts store and back.
1 - Disconnect the battery.
2 - Remove engine cover (10mm standard wrench needed). There is a single hex head bolt on the back side towards the left that needs to come out. Then the whole piece will pop off. Give it a gentle tug - there are two plugs that the cover will snap back in to once you're ready to reassemble.
3 - Take note of your belt path for the serpentine belt, because it's coming off. It will be the belt that is actually running over the alternator. I believe there are five pulleys on the 2.0 that this belt drives.
4 - Remove the black hose that is over the alternator; it should clip into a black metal bracket. I found that taking a small flat head screw driver and pressing the clip helped me to get it to release. If you look to the back side of this metal bracket, you'll see that it just snaps in. Once you've gotten it loose from the bracket, just move it so it's up and out of your way.
5 - Remove the serpentine belt - the tensioner has a handy little section that a 15mm wrench fits nicely over (little pertruding square that you can hook a wrench over). Pull that towards the front of the car, and you should feel the tension come off the serpentine belt, remove the belt...don't forget to make note of the path for the belt!
6 - Remove the tensioner that was holding the belt. I believe it's 3 bolts; you'll need a 15mm socket to remove these. Once the bolts are out (approximately 3" in length), the tensioner should come right out and to the left of the alternator. This is a good time to check the bearings in your tensioner. Give it a little spin, if it's quiet and spins freely, then it's good to go.
7 - Remove the alternator. There are two bolts (15mm) that are holding the alternator in. Remove these, and you'll need pry tool to get the alternator to release. There is a space at the top where the top bolt comes out, it's the most sturdy place to push the alternator towards the front of the car. If it doesn't want to budge, a little shot of WD-40 will break it loose.
8 - Once your alternator is loose, pull it straight up and it should release from the bottom. Turn the alternator to it's side, and remove the cable that is connected to the battery (10mm). It is imperative that your batter is disconnected here. If that wire is live and it hits the metal, it's going to instantly weld.
9 - Insert your new alternator - it should slide into right into where the original came out.
10 - insert the two alternator bolts. The bushings on these particular alternators are not fully installed - they finish when you screw in the bolts. Takes a little while, but they will tighten. It calls for 18lbs of torque, I tightened mine until tight and a little. I didn't go crazy tightening the bolts down (checked a week later and still tight).
11 - connect the batter cable (10 mm socket or wrench)
12 - Reconnect the tensioner (15mm sockets)
13 - (Helps to have a buddy here) - utilizing that diagram you drew for the belt diagram, replace the serpentine belt. I found that going from under the car while someone above is releasing the tension is the easiest way to put the belt back on. You have full visual of all the pulleys to ensure that they are all seated properly with the belt.
14 - Replace the engine cover (remember the two plugs at the front), and use the 10mm wrench to replace the engine cover bolt.
15 - Reconnect the battery.
16 - Replace the black hose that you moved aside to get the alternator out.
Hope this helps - if anyone needs pictures, let me know and I can post those to show what parts I'm describing.