Voldemort killed them with the Avada Kedavra. I thought everyone knew that. He killed them, trying to get to Harry, and the Killing Curse reflected off of Harry because of his mother's प्यार and hit Voldey. Come ON!!! I'd tell आप more, but that'd be a spoiler.
आप got it all wrong, folks. It's Santa Claus that killed James and Lily. He wanted to give gifts to Harry but when reminded this was only हैलोवीन and not Christmas, well, he got kinda pissed off.