A Beginner's Method
to Solve The Cube
Basics
Solving the Cube
 Step 1: Bottom Edges
 Step 2: Bottom Corners
 Step 3: Middle Edges
 Step 4: Top Edges
 Step 5: Solve Edges
 Step 6: Position Corners
 Step 7: Solve Corners
 Done
Extras
Step 2: Solve Bottom Corners Except One

Solve three of the four bottom corners. Step 1 and 2 have solved the bottom layer up to one corner. 

Basic idea
We want to move corner cubies withouth disturbing the white cross. Use Y = FRiFiR to swap corner cubies from the Ulayer into the Dlayer along a vertical edge. Choose between Y and its inverse Yi to get the orientation right at the same time.
Details
There are two main cases:
 The bottom corner cubie is in the top layer.
Use U moves to move the corner cubie into the position vertically above its target position. There now are three cases depending on the orientation of the cubie:
Notice that in the first two examples we pick Y or Yi so that the first quarter turn moves the cubie into the solved position, which is also the position at the end of the move.Use Y = FRiFiR.
Use inverse Yi = RiFRFi.
Use Y three times.
 A bottom corner cubie is in the bottom layer, but not positioned or
oriented correctly.
Use Y or Yi to swap the cubie to the top layer and proceed as in 1.
Pick Y or Yi to get one of the simple subcases of 1.
Comments
Which of the four corner cubies is left unsolved is up to you. Usually, some corners are more easily dealt with than others, so do them first. The remaining corner cubies might even move into a better position at the same time.
Alternatives
We suggest the 3*Y move above because it is straightforward. However, shorter moves are possible by using Y along different edges or using other elementary ideas altogether.

 Example: Corner in Ulayer with white facing up Do the Ymove along the upright edge from front to back (RUiRiU). Do the Ymove along the upleft edge from front to back in reverse (FiUFUi). The last Ui is irrelevant, so we need 7 elementary moves compared to the 12 moves in 3*Y. 

 Example: Corner in Ulayer with white facing up If you count U2 as one move, you can also do this in 6 moves. Do the Ymove along the upright edge from front to back without the last U, which is RUiRi. Finish with FiU2F, which picks up the missing U.
