I very much fear that it was Willie, if anyone who probably taught Barnabas how to drive.
If you'll recall, when Willie leaves off petty theft, harrassment, and goes off to work for that stalwart, decent, upright citizen, Mr. Barnabas Collins, his cover story is that Mr. Collins had some automotive trouble and that Willie was able to fix his car.
So with that kind of excuse, that would probably let off one of the Collinsport citizens from teaching him how to drive.
My guess is that Willie probably tried to teach him. Barnabas got impatient ("If you can drive, than surely anyone can"), and decided he knew how to drive.
I also strongly suspect that he has to be a really annoying passenger. One of those people who keep trying to tell you how to drive (remember this is a man who decided he knew best about Julia's formulas and medical treatment).
Which would explain why Barnabas seems to get into a fender bender anytime he steps into a car.