I'm assuming full familiarity with the 3x3x3 solution and despite the fact that it won't be used too much, also with the 4x4x4 solution. Notations similar to the 4x4x4 versions.
Now we have 54 center pieces, 8 corner pieces and 18 edge pieces. I'll call three edge pieces that are adjacent a "wing". Notice that an edge can be mid-wing (will be in the middle of the wing), or side-wing (not in the middle of the wing). Also notice that mid-wing edges will enver swap with side-wing edges and vice versa.
As before, in a motion, if the letter is written as is, it means a clockwise turn. Otherwise, it's counter-clockwise. Also, usually I'll try to keep white face on top.
As with Rubik's Revenge, we will first get the centers correctly, then fix up the wings, and go on for a 3x3x3 solve.
Center strip:
Side strips
The point here is to bring up all the remaining white center pieces to one of the F-L-R-B sides (and not D), without ruining the center strip. Then you form strips and push them up.
We apply the same steps as above, making sure not to ruin the white center (see the Revenge's solution how we do that). We arrive to this:
Once you have the two opposing centers (white and yellow), you are now restricted to (Uu) and (Dd) moves, - i.e. just rotate on the horizontal axis (and of course, simple face moves, F/D/B etc.). You'll get two adjacent centers, by first forming a 1x2, then 2x2, then 3x2, and then 3x3. Here's an example:
After this, with a similar method, you get the adjacent center - without ruining the first (blue) center. This is a bit more difficult, since you're restricted to face moves and (Uu) (Dd) moves, but the technique is very similar to step 2.
These are probably the most difficult. I'll list a few tricks, that should help you out.
Strip-swap: Just swaps two adjacent strips, no effect on the rest of the cube.
Actually, the trick above, and some resourcefullness is enough to solve this part. However, there are some shortcuts, supplied by bigcubes.com
Lightning bolt: When you have a lightning-bolt with 1x2 in adjacent face
L-shape built with a single edge in adjacent face
Edge-swap: swapping a single edge
Corner-swap: swapping a single corner
Here on, we do only face moves, unless instructed otherwise. Our main tool will be the following move:
Notice that this rotates the orange, blue and white side-edges, without affecting any centers and any other wings than these three. Use this repeatedly (it'll take quite some time), until you have all wings (or all wings but two) fixed. Notice that like the Rubik's Revenge, wings need not comply to centers, they must just match within themselves. Also, of course I know there is no such thing as cyan-cyan edge, but you get my point. Also, make sure that all wings have their middle-edge connected to a correct side-edge at least on one side before completing all the wings.
Now, you should either have everything fixed, or in the following position:
If you do end up in the said position, the above move also fixes it. As in Rubik's Revenge, this move also unfortunately needs to be memorized.
Now, you go on solving this as a 3x3x3. Unlike the Revenge, you can't run into anymore parity bumps at this point. You're done! :-)