1995 SAAB 900 Alternator?

Boyfriend was driving to pick me up from work and the car was fine. While he was waiting on me, he still had the car running and the air conditioner as well, as it was sweltering. He detected a slight hint of burning wire, so he turned the car off. I got in the car and he started it and we left for home. Everytime we went over a speedbump in the area where we live, the red triangle light would come on and the car would ding. Well, we thought it would be ok for him to drive it to work (as he only has a mile or so to drive) and we could look at it when he got home. Well, on his drive home, he got about a quarter of a mile from the house, he turned at the stop light, and it died. He got it pulled off the side of the road and walked home. There was barely enough juice to run the hazard lights. Then when we tried to start it, there was nothing. A kind gentleman happened to stop and he gave us a jump. We let it charge for a bit and he said he would follow us home to make sure we made it. We didn't get 500 feet before the car lights dimmed again and it just died. We did, however, make it into the drive of the addition we live in, and it is downhill most all of the way, so we coasted home. The car now sits in the driveway and we need to find out what is wrong with it. We can't afford what a shop here would charge us so, we need to see if it is something we can replace ourselves. I do have some mechanicing under my belt but unfortunately for me it is on mid 70 to mid 80 Chevys. So anyting newer or foreign and I am a little more worried I will screw something up if I don't get the proper information to get it fixed. That is why I am here. So thank you in advance!

Vee H in Asheville