Planning a trip to Germany going from Munich to Stuttgart/Black Forest. Is it better to stay in Stuttgart and do day trips to Calw and other Black Forest spots? If so, would you advise renting a car and driving to those spots or are there trains or day tours that would be better?

Car would be best and Tubingen would make a nice smaller city base - university town and rather cute. But trains also go thru Black Forest to places you can get out and walk, etc - check www.seat61.com; BETS-European Rail Experts and www.ricksteves.com for insights on German trains and where to go. Freiburg would perhaps be a better base for Black Forest?

How difficult is driving for a hesitant American with little European travel experience?

Trains from Stutgart to Calw run about every 20 minutes. It takes about 1 hr.
There are good train and bus connections to all small towns within the Black Forest area.
If you want to visit the Black Forest, stay in the Black Forest and not in Stuttgart (which isn't particularly scenic).

I would not worry about driving in Germany and by far the best way to really tour places like Black Forest. Really just about like at home - universal road signs - just nice to stop off at whim at some small village or market, etc. For Munich and Stuttgart those cars are useless so maybe take train to Stuttgart then car around Black Forest, yes basing in a smaller town that is more car friendly. There are many neat Black Forest towns.

Stuttgart isn't a good place to tour the Black Forest from. I agree with PalenQ you ought to look for a small town in the Black Forest, perhaps one with a railway station. You don't necessarily need a car.