1989 911 Alternator problem
 

I accidently ran my battery down by leaving the radio on over the weekend as the car sat in the garage while I went out of town. I took the battery to Advanced Auto and had them test it. They said it was low but not completely dead. They charged it for 35 mins and said it would be good to go. Installed the battery and ran the car around town and it died again after about 20 miles. The car was operating well before all of this. Its seems like the alternator is not charging it now but I dont know for sure. I am good with mechanicals but not so good with electrical issues. How can I test to see if the alternator is in fact bad? Or, should I remove the the alternator and take it to a local rebuild shop for testing?

A simple volt meter ( i'm sure Advanced must have them) on the battery will tell you real quick.
At idle around 13-13.2V 2000 RPM around 13.8 or so.
Is the alt. light on?
How old is the battery?

the battery is less that one year old.