Can anybody tell me a general method for evaluating path integrals? I read the section in the Shankar on them and have an idea but I'd like to have someone else explain the procedure to me just to be sure that I'm on the right track. Also, can someone recommend a good reference on the subject?

Uh, I would guess that the simplest general way of evaluating path integrals is exactly the way that's normally taught: find a parametrization for the path, convert the integral into an integral in that parameter and integrate.

Of course, if the integrand is exact: if there exist a function having that integrand as differential, then the integral is independent of the path and you can simply evaluate the function (the "anti-derivative") at the endpoints and subtract.

Am I missing something here?

Am I missing something here?
he mentions Shankar, so I think it's clear that he's asking about the Feynman path integral