3^4

Roice Method

This method is the 4D version of the "ultimate solution for the rubik's cube's.
check it out here: [1]

Ray Method

This method is the 4D version of F2L, and if you know how to improve the last layer then e-mail me with suggestions.
You should know how to do Roice method before doing this. methods marked with a * are annoying to do if edge and corner rotation shortcuts aren't available. (MC5D and 7D)
Summary
1. cross (on hidden cell)
2. f2l (2C/3C pairs)
3. s2l (3C/4C pairs)*
4. foll
5. eoll
6. fepll*
7. coll
8. cpll
step 3 and 5 to 8 require knowledge of Roice method

Method:
1. Make the cross on the "hidden" cell. In other words, make it on the cell not visible.
2. If you don't know how to do f2l on the 3^3, check it here: [2] This step is solved in rings of four, meaning first you solve the four equator edges (XY plane,) then rotate an unsolved ring to the equator and solve that. Lastly, you rotate another unsolved ring to the equator and solve.
3. This step is kinda annoying. Once you get an edge-corner pair (doesn't have to be solved) on the top cell, you solve by orienting the edge then doing an slice turn to match the edge with the corner, moving the solved pair away then reversing the slice turn. Also can be expressed as x y x' where x is the slice setup and y is the "moving away" turn. After that you do another x y x' but with x being a "call setup" and y being a 3-cycle insertion (A Perm.) I might as well pass an example below.
4. This is easy. Just use the alg used on the n^3 to orient the top cross (F R U R' U' F' or something like that)
5. Orient the edges by doing x y x', where x is a few setup moves and y a corner OLL alg. if only one edge is unorientated use Roice method.
6-8. Roice method time. You might want to create a few shortcut macros here.

Sheerin-Zhao method (hybrid)

This method (In ray's opinion) is pure awesome
1. cross
2. f2l
3. s2l
4. oll
5. fpll
6. pll

Method:
1. Make cross, see ray's method
2. Make f2l pairs, see ray's method--but, it doesn't matter what order you do, just don't confuse yourself
3. Find a corner with the hidden cell colour. Then find the corresponding edge (or vice versa.) Put them on the same plane using <RR,I-> moves, and orient the edge or corner using an OLL from the 3^3 (I use sune or anti-sune.) Then put the pieces together using <RR,I-> moves, and insert using setup and <RR,I-> moves.
4. Orient the faces then edges using OLLs from the 3^3. Try to get as many corners oriented as possible as well. Use a rotation then <RR,I-> versions of the OCLLs to orient the corners.
5. Match the faces of the top (I) cell. You may want to use an U-perm.
6. Solve the top (I) cell like a 3^3 by using <RR,I-> moves.

Notation and <RR,I->

It's the same as normal 3^3s, well kind of. There are 8 cells, UDFBRL and IO, with O being the hidden cell (out)
Each cell has 6 ways to rotate, UDFBRL.
so the cell is first stated, then the rotation. ex. RR,IF,RR,IF',RR' If you don't care about which way the cell rotates, use - (for blank, this is used for writing move subsets)
notation is pretty inefficient, so I don't use it a lot
<RR,I-> moves mean to only use RR and I moves (for I, you don't care about which way you rotate. <RR,I-> moves are pretty epic for blockbuilding, as it doesn't affect many pieces. Idea by Matthew Sheerin.