Watch this how to video to figure out how to solve the 4x4 Rubik's Cube Revenge. So, get out your Rubik's or Eastsheen Cube and watch this tutorial.
First, get the centers down. Then, pair each individual edge with one short algorithm. Then, remember how to solve the 3x3 Rubik's Cube, because it's pretty similar from here on. Then, learn how to get away from parity errors. Watch all four of these videos to see the how to to solving this 4x4 Cube.
You're probably going to need to learn about Rubik's Cube notation before trying to solve the 4x4. Wait... it covers notation, too!
Soon, you'll be on your way to speedsolving, won't you?