Solving the 4x4x4 using the Reduction Method
The Reduction Method is a method for solving big cubes. The basic idea is to first solve all six centers to create one large center on each face. Next, pair all edge pieces to create 12 large edges. At this point, you can solve the puzzle like a 3x3. The only difference is that on even cubes (such as the 4x4), there are a few "parity" situations that cannot occur on a 3x3.

Solve the CentersThe first step is to solve the centers. This is a mostly intuitive step, so the best way to improve at this step is to just practice. 

Pair the EdgesIn the second step, you'll pair the matching edges. I solve the edges two at a time. It is possible to do this step with six edges at a time or to do other things, but I won't get into that here. In general, this step is pretty easy as it takes only a few moves to pair edges. The toughest part in this step is the lookahead to eliminate delays between pairing. 

3x3 StageIn the third and final step, you'll solve the puzzle as a regular 3x3. There are two parity algorithms that you need to learn, but other than that, it's pretty standard. 