Seems like if a comet were headed to earth, the best bet would be to get as much mass into space, and shoot it as fast as you can in order to knock it off course.
Much less fun than a Bruce Willis shlock disaster movie, but seems pretty practical.
So you're probably talking about one or more kinetic impactor missions to try and deflect it billiard ball-style. Before those actually launch, the laser-ablation strategy seems like a pretty attractive option to do in parallel. You'd build an array of lasers that ablate the surface of the asteroid, ejecting material that works as reaction mass. Northrop has 100kw solid-state lasers working right now: http://optics.org/news/1/7/13
Seems plausible that you could get something up and running quickly to see if it would work. Before either scaling it up or dropping back on the riskier impactor missions.
(No practical confirmation, of course, but the idea is supported by a lot of prominent physicists.)