How to defend against an asteroid

The first and hardest method is the Armageddon approach- blow it up with a nuke. Depending on its size, many bombs might be necessary to break it into smaller pieces. Even then, the larger chunks would still cause a lot of damage and probably throw up enough dust to disrupt farming for a while.

Next we have the Big Push- use a nuke to push it out of the way. The hitch with this is that a nuclear explosion by itself would not produce much of a push. The blast from a nuke comes from air being heated rapidly and then expanding. If you wanted to use a nuke to push something in space, there would need to be some gas or liquid with the bomb to get hot and expand. 

I don't think attaching rockets would work. Although rockets are the only way to get things in orbit, they are not very efficient. You'd have to attach many, many rockets to get any kind of push. 

The last, and I think most practical option, is to build bunkers and shelters to ride out the impact and effect of decreased sunlight. Using technology like cloud seeding might be helpful in washing the dust out of the air. 

As an honorable mention, I'll mention a thunderwell type device- this uses a nuke to create steam which propels an object at a fantastic speed. It was discovered during a nuclear test when a hunk of metal was accidentally blast miles and miles into the sky. The hunk traveled so fast that it partially melted.