Since the 4x4x4 cube can be solved most largely with the same method as the 5x5x5 cube, I won't repeat the whole solution but instead only point to the differences and peculiarities of the 4x4x4 cube compared with the 5x5x5 cube.
Hint:
This solution is made for beginners who want to solve the 4x4x4 cube the first time.
If you're already able to solve the 4x4x4 cube and you're searching for a effective and fast method, I recommend to try the
Yau method.
The side pieces and edge pieces can be solved the same way as at the 5x5x5 cube. However, when you're solving the 4x4x4 cube there are the following difficulties:
Applet 1a 
At applet 1a you can see that only two colours of the
corner red/blue/yellow
match with the colours of the side
pieces (red and blue) but instead of the yellow
side pieces
there are the white ones. By the way, it doesn't matter which 2 sides change
their places. Instead of white with yellow you could also exchange red with
orange or blue with green.
Tip: When you've solved the cube one time, you should memorize the exact
position of each colour. Then you don't have to orientate on the
side pieces
and corners when you
solve the cube the next time.
The concluding solving of the
side pieces
explained in section 3 of the solution for the 5x5x5 cube can also be done like
at the 5x5x5 cube, but since there are much less possibilities how the 4x4x4
cube looks like now (compared with the 5x5x5 cube), I will explain every
conceivable possibility in the following.
There are 3 possibilities how the
side pieces at
one side of the cube can look like:
Since the 3:1 pattern can only be simultaneous at both sides, there are altogether only the following 4 possibilities:
Applet 1b 
Applet 1c 
Applet 1d 
Applet 1e 
Applet 1f shows the turn combination of applet 1e with the inter steps which are necessary to avoid mixing up the already ordered edge pieces. The side pieces are mixed up with the last 180° turn but this doesn't matter for the moment. They just have to be moved in the right position for solving of the next two sides.
Applet 1f 
When you now try to complete solving of the cube, maybe the cube looks like shown in one of the following applets:
Applet 1g 
Applet 1h 
Applet 1i 
Applet 1j 
These are peculiarities of the 4x4x4 cube: At the 3x3x3 cube it is impossible
that only 1 edge
piece is "twisted" wrong (applet 1g) while the others are all twisted right
(except that it was taken to pieces and put together wrong). It's also impossible
at the 3x3x3 cube that only 2 edge
pieces are at the wrong place (applet 1h, 1i). This is not the case for the
outer
but also for the middle
edge pieces of the 5x5x5 cube because they can only be mixed up the same way
as at the 3x3x3 cube. Therefore you can orientate on the
middle
edge pieces when you're solving the edges of the 5x5x5 cube to be sure that
all edge pieces
are twisted right. At the 4x4x4 cube this is not possible because this cube has
an even number of layers and therefore the
middle
edge pieces are missing. Therefore you can notice whether all
edge pieces
are twisted right just when you've solved the cube almost complete (at least
I know no method to notice this earlier).
To solve the cube when 2 edge pieces are twisted wrong (as shown in applet 1g)
you could use the method explained in the solution for the Professor Cube
section 2 (applet 2i + applet 2j), but this has the great disadvantage that
there are only the edge
pieces twisted right but the whole cube is rather in a mess after that. You
reach the goal much faster when you use the combination of turns shown in applet
1g. This combination  in contrast to all other combinations on my site  is
not thought up by myself but by Frédérick Badie, I have found it
on the page of Stefan
Pochmann
In the second case (each two edges on the wrong place) please use applet 1h or
1i. At applet 1i first 3 "setup moves" are necessary to place one wrong edge
opposite to the other wrong edge to get the same initial state as at applet 1h.
Then the identical moves as at applet 1h are following; finally you have to
reverse the first 3 setup moves. Applet 1h and 1i are also from the page from
Stefan Pochmann.
Depending on which solution you use, it's also possible that there are finally
not exactly 2 edges
but exactly 2 corners swapped.
In this case Applet 1j will help you. Applet 1j consists of 2 parts:
The first 14 turns swap the 2 wrong corners
and also 2 edges.
All you have to do now is the same as at applet 1h.
