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 3: Solve Middle Edges Except One
 Solve three of the four edges in the middle layer. We don't solve the edge above the unsolved corner. After step 3 we have solved the bottom and the middle layer except for two cubies in a vertical column. 

Basic idea
Use the Ymove to cycle edge cubies from the top layer into the middle layer. In preparation of the Ymove, turn D to move the remaining free bottom corner into the corner position that is affected by the Ymove. Undo the Dmove when done.
Details
 The edge cubie is in the top layer.
Focus on an edge cubie in the Ulayer without a yellow sticker, say the greenred edge cubie. Do a Uturn so that either the green or red facelet match the face of the cube. Then there are two cases:
We prepare with Di so that the Ymoves only involve the free bottom cubie, and we restore the bottom with D. Pick Y or Yi so that the first quarter move 'does the right thing'.Use Di Y D.
Use Di Yi D.
 The edge cubie is in the middle layer.
It doesn't really matter whether we use Y or Yi here, but one of them may give a shorter continuation.Use D Y Di to move the edge cubie to the top layer.
Continue as in 1.
Comments
The basic Ymove is just what we need  but don't forget to prepare/reset the bottom layer.
Alternatives
For simplicity we only use the Ymove in the standard orientation, which starts 'down the frontright edge'. It is worth practicing the Ymove 'sideways', because we will need it later, and because we may save a quarter turn at the end of the Ymove. Here are two examples:
Y along upright, R Ui Ri U, 
Y along upleft, then 
Notice that the oneturn savings requires a flip in the starting position compared to case 1 above. Do you see how the last example can be reduced to six turns? (Counting U2 as one move, compare alternatives for step 2.)