0. Learn the moves
L = left face, R = right face, U = up face, D = down face, F = front face.
L =
L' = 
R =
R' = 
U =
U' = 
D =
D' = 
F =
F' = 
Since this is an easy method only 8 moves are required. 4 faces clockwise (indicated by the letter of the name of the face) and 4 counterclockwise (letter with apostrophe). Moves that require 2 times the same face, for example F F will be represented as 2F. Double counterclockwise and clockwise are equivalent for example U U = U' U' = 2U The
key to solve the cube is to look at it from one angle of reference without turning it around!1. Make a white cross
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To make a white cross, intuitively place the white pieces around the central white piece. Ignore the rest of the pieces. Beware that the central pieces (pieces with only one coloured square), have always the same position (white opposite yellow, blue opposite green, red opposite orange). That means green is always to the left of red when white is on top, etc. Therefore the cross has to be made so that the pieces follow that order with white cross on top (counterclockwise: green, red, blue, orange):
1.1 Not intuitive (if intuitive skip to step 2):
To find the order you need keep turning the top face until you have the missing piece in the desired place. That is the move U or U' as many times as needed. If the piece is facing frontwards do the following.
-- F U' R -->
-- F' U' R -->
-- U' R -->
-- 2F U' R -->
That last one can be done alternatively on the other side by simply doing U L' which is the mirror of U' R already shown. Most mirror positions in the cube can be done by executing mirror moves. Mirror of F U L R is F' U' R' L'.
2. Complete the first layer
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Rotate the bottom layer with D or D' as many times until a corner piece with the three colours between the cross is underneath where it should go. There are 4 scenarios: the white on the corner piece faces the front, the white faces the right, the white faces down, or the white is in position but rotated. Note that I use green and red for all examples but the same applies to all other corners with other colours, just chose two colours. Most of these can be don with R, R', D and D' alone. This section applies for the 2x2 cube identically.
-- F D F' -->
Doing F or F' can be difficult for the fingers. The previous sequence can also be done with D' R' D R.
-- R' D' R -->
White on corner pice faces down (not seen as it is facing down), take it to previous step:
-- R' 2D' R D -->
Corner piece in the corner but wrong rotation:
-- F D F' D' -->
Doing R' D' R D on the previous sequence puts the piece facing down (sequence shown above).
-- R' D' R D -->
Pro Tip: The corners of the cross (first layer) can be solved with the cross on the bottom layer so that it is easier to see the top layer and the cube is ready for the next step (important for speed solving).
3. Complete the middle layer
Once the first layer is done, put the cube upside down so you can see the mixed pieces and the white on the first layer is at the bottom. Again I use here green and red faces, same applies for all others.
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Rotate the cube or the top layer until you find one of the next 2 cases (which are very similar):
-- U R U' R' U' F' U F -->
-- U' F' U F U R U' R' -->
If the piece is already in already in the middle layer but in a wrong position, take it up to the mixed top layer but executing any of the above sequences (U R U' R' U' F' U F) and the piece will come out, then just do U or U' until the cases above show up.
-- U' F' U F U R U' R' -->
Note that the piece can be in between any other two colours (not necessarily green and red), repeat all previous steps for all other colour pairs until the middle layer is solved.
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4.1. Four yellow corners
First we will focus on making all the corners yellow (this is identical for the 2x2 cube), there will be other yellow pieces in the cross but we will ignore them for now. The initial state can have 3 cases for the corners: 2 yellow corner pieces facing the top, 1 yellow corner piece facing the top, 0 yellow corner pieces facing the top. One algorithm and its mirror is all it is needed.
4.1.1 One piece up:
-- R' U' R U' R' 2U R -->Mirror:
-- L U L' U L 2U' L' -->4.1.2 Two pieces up (same algorithm as in 4.1):
-- R' U' R U' R' 2U R -->
-- R' U' R U' R' 2U R U->
- R' U' R U' R' 2U R 2U->4.1.3 Zero pieces up:
-- R' U' R U' R' 2U R U'->
-- R' U' R U' R' 2U R -->4.2 Complete all top yellow
There are 3 possible scenarios, one algorithm alternates between them and leads to the H position, which is solved by the same algorithm,
-- L R U R' U' L R' F R F' 2L -->
-- L R U R' U' L R' F R F' 2L U-->
-- L R U R' U' L R' F R F' 2L -->5. Orient the last layer
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5.1 Orient the corner pieces
Find a face that matches 2 aligned corner pieces on the top layer in this case is green again, it can be any colour. Position it as in the diagram and execute the algorithms. If there are no 2 pieces aligned execute anyway and then one face will be aligned.
-- U L' U R' 2D R U R' 2D R L -->
Now find a face that matches the central piece with the top layer (again I am using green, can be any colour). If there is no matching face with the top yellow layer, execute the algorithm any way. Match again and repeat until the cube is solved. This algorithm rotates 3 middle pieces counterclockwise (try on a solved cube to see the effect), its mirror algorithm rotates them clockwise. Tip: Skip first and last step (U' and U) by starting with the aligned face on the back (B) of the cube.
- U' R U' R U R U R U' R' U' 2R U->
As you practice the algorithms above, you will notice that remembering the mirror algorithms or skipping the steps with black characters can save you moves and time solving the cube. Good Luck!
A. Pro-tip for cross upside down:
-- R U R' --> piece down
-- U R U' --> piece down