Here is a small step by step guide, based off of the Petrus Method, that may help you:
#1 - Make the cross on the first layer.
- To do this, first orient 3 centers in the proper direction (so you have yellow to blue, blue to red, red to yellow) on the 3 edges going clockwise.
- Now insert (using F2L,) the corner with one of the edges (yellow, red, or blue)
- Repeat the step above for the same corner 3 times (once for each edge).
#2 - Build the corner and 2 outer edges of 2 colors
- Place together one corner and edge, and then place the second edge and insert them into place.
- This may take some practice. You may end up with it inversed, but it is not a parity. Just reverse one of the edges with the following algorithm: R U2 R' U2 L U' L'.
- Build this on 2 of the colors from your 2x2x2 block (red/blue/yellow in this case).
- Insert the last F2L pair if required.
#3 - Make the last layer
- Make sure that the edges are correctly oriented, and detemine if you have the bar case or the crooked bar case.
- Think of the top layer as if it were the regular Rubik's Cube. Turn the top layer 45 degrees so you have it facing you just like a side on the Rubik's Cube.
- Remember! There are 2 sets of 2 identically colored edges! Use this to your advantage (U-perms).
- To rotate one center 180 degrees, use the following algorithm: [R U R' U] x6. This will keep all other pieces oriented.
- To rotate one corner 120 degrees, use the following algorithm: [L' U' L U, meant to be Lefty Alg] [L' U2 L] [R U R' U R U2 R'].
- Some notable algorithms from 3x3x3 include:
- 2-look OLL cases (Sune/Bar/L-shape)