I have some more to add...I just finished a paper tonight on a Truffaut film for a class, so it's on my mind.
All of these filmmakers were heavily influenced by novels. They were also aware of the Italian neorealist movement. Andre Bazin, was kind of a mentor to a couple of the filmmakers, and he has his own personal theory about what cinema should be if you are interested in reading about that. Though, the filmmakers that were influenced by him, went away from his ideas pretty quickly. Not that they were bad, the french new wave filmmakers were just big on doing things their own way, I guess.
It's also important to know that what they were reacting against was the 'perfect' French studio films that came right before them. And even more than that, they were against the screenwriter as the chief artistic person on the set. They really stressed the director as the author of the film. Which to some extent is dying today, because filmmaking is obviously a collaborative art.
Stylistically, these films were known for their long takes, moving camera, jump cuts, SELF-REFLEXIVITY (eg. looking at the camera, zooms, etc, anything that draws attention to film as a medium, meaning that they were very aware that what they were creating was a reconstruction of reality). This is in opposition to the invisible, illusionistic, Hollywood style filmmaking. But as I said in my previous post, they use a lot of traits from Hollywood films.
As others said, John Cassavettes is a great American example of French New Wave style.
If you're looking for directors, there's: Malle, Chabrol, Resnais, Varda, Truffaut, Godard, Rohmer, and Rivette. Just a list of some. Malle and Chabrol were kind of pre-cursors to the movement, but the others all played a large role.