The best woudl be something akin to a solar powered engine of some sort. Maybe a drill that would mine from one side, then launch chunks out the other. The chunks would be small enough to burn up if any of them happened to come our way, but otherwise this would be something that would take some time. A nuke? I would have to check my phusics on this one, but there is not a heck of a lot of mass associated with one of those, so it would not be able to change the course of the center of mass of a large object. I think the only thing you could do would be to use it to split the asteroid up and send its pieces in opposite directions (its center of mass would still be headed for earth, but the two halves, or however many sections, would just go around us....). Things don't work quite the same way they do in the movies. Not many scriptwriters or directors ever did well in Physics.....