There is actually no difference between solving the 4x4x4 as with a 3x3x3 once you have solved the centers and the edges.
Simply treat the inner slices as a single slice and do everything the same as you would with the 3x3x3. Check out the
image below to see what I mean.
I will follow the same processes I used in the 3x3x3 section and display them to you below.
Note that I am not showing the algorithms used in the examples, they wouldn't be useful for you to use unless your cube happened to
be aligned exactly as mine.
First, let's move the top edges into place, then the top corners. 
Now let's solve the second layer. 


Now I flip the cube over to put the bottom corners into place and shift the last edges around. 
We've ended up in the fish pattern, so we apply the algorithm to solve the cube. 


It may be that you have come to this point and found you have a parity issue. A typical parity issue is having all the pieces
in the right place but facing the wrong direction. Even numbered cubes have a few outcomes which are not possible on a 3x3x3.
Using my methods I usually only see two on a regular basis. One I call a flipped edge and the other I call an inverted H. Over at
www.bigcubes.com they call these 'single parity fix (oll)' and
'opposite edge pll parity' respectively. I'm going to show these two below. If you find yourself in a different parity
you should click the link to visit their site to find the solution that fits your situation.
Flipped Edge Parity. 
Inverted H Parity 


r²_B²_U²_l_U²_r'_U²_r_U²_F²_r_F²_l'_B²_r² 
r²_U²_r²_(Uu)²_r²_u² 
Well, that's it, you now have a fully solved cube, congratulations!. Now why don't you try moving up to the 5x5x5.
