Vampires can only die when they are cut up into several pieces and then every single piece has to be burned to completely remove every sign of them. Nothing else works. And, no , the sun doesn't burn them.
ELABORATING: the above answer is only true of Twilight vampires. Methods of death include, exposure to sunlight, wooden/silver stakes to the heart, breaking or severing of the head, lighting them on fire, silver bullets, and if you kill the "creator", you kill every single one he/she created. Vampires can be severely hurt by, religious objects (crosses holy water), garlic, and also by stealing their "coffin", well not so much the coffin , but the dirt of their homeland in which they sleep in.