T The movie Armageddon focuses around a team of rough drillers being roped into saving the planet from an asteroid the size of Texas by an obviously desperate NASA. In the movie NASA recruits a group of very wacky drillers to fly to an asteroid and drill deep around to slide a nuke inside and spit it in half with the resulting explosion. Said explosion would then split the asteroid so that both halves would conveniently miss earth on either side. Aside from the obvious flaws and the even more obvious flaws, they manage to save the earth after Murphy's Law has its way with the crew. True to 90’s fashion the movie is full of big explosions, love and mathematical impossibilities.
Now however, let's look at an actual plan that the good men and women at real life NASA have come up with to save our planet with actual science rather than Bruce Willis. One proposed idea would be an Asteroid Gravtity Tractor. This method would put a large, heavy space craft matitaining orbit over an asteroid, the ship and the asteroid both gravitationally attract each other, thus if the ship resist the force towards the asteroid the net effect would cause the asteroid to accelerate in the direction of the spacecraft. Such a craft would use a thruster, such as an ion thruster, to counter the gravitational force of the asteroid.
This method has advantages and disadvantages, it would have to be deployed years in advance in order for the slight change in the asteroids path to achieve the required amount of deflection. This process is certainly slow, but it is steady and reliable. Furthermore this method can work on any asteroid regardless of the asteroids composition, rotational speed, or surface terrain as it does not need to come in contact with the asteroid. A Gravity Tractor may not be as flashy as Bruce Willis, however it could work and probably do it in less time than it took Bruce to push the detonator.