It depends on the car. And the procedure is controlled on a state-by-state basis. (But there may be a series of Federal EPA tests: see below.) Some models are more acceptable than others. I just imported a 1989 VW "Tristar", which is a vanagon-based pickup truck that was never sold in the U.S. It came from Sweden by way of Germany. Read my post about importing it here:
http://www.thesamba.com/vw/forum/viewtopic.php?t=227031&highlight=tristar
I talk about the whole procedure about 2/3rds of the way down page 1. I'm in California, so it's hardest to do here, but it was still easy. It just takes time. But again, make sure the car you want can be made legal once it gets here. Find a registered importer in your state and do a lot of research.
BUT WAIT! READ ON: One thing that made it easier for me is the fact that my Tristar is full time 4-wheel drive. Usually, a car has to pass a Federal EPA smog test. However, the Fed's can't test a full time 4X4, since their equipment can't handle 4 spinning wheels. Therefore, I was exempt from the federal test.
A friend bought an identical 1989 Tristar, except it's 2-wheel drive. He has been trying to pass the federal test for 2 years. The hang-up is one of tests they do (I forgot the name) where they put a hot pad on the gas tank and test for escaping gas fumes. If there are any, you fail. He just can't get the fuel system airtight.
My 4X4 is exempt from this also, because on the 4X4 vanagon, the gas tank is inaccessible to the hot pad. I lucked out, as I found out about all this just a couple weeks ago from my disheartened friend. I got my pink slip in the mail last week!