The 1x4x4 is a puzzle that has not been invented or mass-produced yet as of June 6, 2010. kcwong707 on eBay sells them, but they are not fully functional. If you would like to buy one, click here. If eBay says the listing has ended, search something like "1x4x4 rubik" in the search bar. Anyways, let's get to solving it.
The algorithm notation is just like the one I use for speedcubing:
U=Turn the top layer 180 degrees
D=Turn the bottom layer 180 degrees
R=Turn the right layer 180 degrees
L=Turn the left layer 180 degrees
Also these notations that you may not know are:
u=Turn both top and middle-top layers 180 degrees
d=Turn both bottom and middle-bottom layers 180 degrees
r=Turn both right and middle-right layers 180 degrees
l=Turn both left and middle-left layers 180 degrees
2U=Turn only middle-right layer 180 degrees
2D=Turn only middle-bottom layer 180 degrees
2R=Turn only middle-right layer 180 degrees
2L=Turn only middle-left layer 180 degrees
z'=Flip whole cube over like this (I used 3x3x3 instead of 1x4x4 to show the alg)-->click here
When performing algorithms, always twist with the 4x4 square facing you.
The first step is solving the outer band. Like the 1x3x3, just position, if needed, let's just say, the blue and green. Solve it by twisting the layer to finish the blue and green side. This only takes few moves to finish and position the side. Last, finish the remaining 2 sides. If you need help, please comment. If the checkerboard case I told you in the 1x3x3 article persists, don't do anything. Also, these are what the checkerboard cases look like. There are 2 cases.
The next step is to solve the centers. You need to learn 2 algorithms.
1. 2L 2R 2U 2L 2R 2U
2. 2R U 2R U 2R
Then, solve the edges. There are 5 cases for this.
1. u r U 2R U r u
2. 2L 2R U 2L 2R U
3. R U R U R U
4.2L 2R U 2L 2R U z' u r U R U r u
5. 2L 2R U 2L 2R U z' 2L 2R U 2L 2R U
Last but not least, if you have the checkerboard case on the outer band, here are the algs for the checkerboards.
1. 2L R 2U D 2L R
2. U R D U R D