The strategy required to directly change the course of a sizeable comet or asteroid depends on many variables. If you have a lot of warning (many years to decades), then a very small deflection may be enough. If you have less than a few years of warning and the object is more than a few hundred meters in diameter, then your options become very limited.

A lot depends on the composition of the incoming object. If it's fairly solid, then we're pretty well screwed. If it's a loose conglomerate, then perhaps a Deep Impact style penetrating warhead could blow it into fragments small enough to burn up in the atmosphere. Or, if we could penetrate and blow off a good sized chunk, perhaps the reaction to that would be enough to deflect it away from the Earth.

If you have less than a year's warning and the object is of any reasonable size, then about all you can do is assume "nuclear attack position #1" (put your head between your knees, look up as far as possible, and kiss your ass goodbye).