I ran into a few accidents on Mafia 2, and ended up with a busted car (and $50 fine). So I quietly stole a car from an alley. Next thing I know, I've got 20 cops after me. How can I steal a car and not get caught before I find a body shop?
First of all you need to evaluate these two choices before try stealing a car:
The first option is the most risky because it produces a lot of noise (most cars have alarm) and it will draw the attention of people in a big range, cops included. I only did a couple of times during my play-through to escape fast from dangerous situations.
The second option is better, if you try lockpicking a car with no people around it usually succeed without being noticed. I am not sure about this but it seemed to me that stealing a car during night is even easier.
If you get noticed by someone during your crime you have no chance then trying to escape as fast as possible. Get the motorway if it is near or choose the straightest city road (this is especially true when playing in winter with no driving assistance) and push the accelerator. It usually allow to escape from chasing cops. If you succeed you have now the possibility to search a body shop with less pression.
Turns out they are infinitely dumb - you can get away a LOT. Here's a picture of what I stole in less than 2 minutes. I took cars from 2 feet away from them.