Saturn charging system

While driving I noticed the little battery icon was illuminated. I checked the owners manual and the next time I drove it the light did not stay on.I had driven about 10 miles when suddenly the windshield wipers slowed down to a stop; the lightsin instrument panel began to dim then everything died. I tried to start it after 15 min or so and it started, the lights and wipers only lasted a few minutes but, the engin kept running. Because it was dark; and raining; I had to pull over and stop. After another 15 min or so again I was able to advance a mile or two until all went dead. I tried starting it the next day, all of the lights and souinds are working but the car won't start and makes a (click. Click) noise like a dead battery. What do you think? I looked at the belts and they all seem fine. Obviously the battery isn't completly dead, should I assume it is the altrernator? What kind of repair work should I seek and from whom in my area? I am in Hayward CA 94544. Can you advise me Please?