Goal: When the first layer has been solved correctly, all the stickers on the top of the cube will be the same color* and those in the first row of each side will match one another, and the centerpiece below them.
Form a white cross
Start by finding a white edgepiece and figuring out where on the topside to move it. The other sticker on the piece should match the color of the centerpiece it is placed above.
Here are some likely scenarios. Use the legend, above, to follow the combination moves notated below each cube. The target position is marked with and X.
T' R T  T T R T' T'  T R T'  R 
F'  T' F' T  T T F' T' T'  T F' T' 
What if the piece is in the first or last layer? 

Perform F or F' moves to bring the edgepiece into the second layer. Then use the techniques described on the left. 
Solve the corners
Move four corner pieces, with white stickers, to the correct position in the first layer.
Flip the cube over so that the yellow center faces up. Look for a white corner piece that is in the top (last) layer. Rotate this layer, using any combinations of T or T' moves, and position the corner piece directly above its target position, marked with an X, in the first layer.
T R T' R'  T' F' T F  R T' R' T T 
What if a corner piece is in the first layer? 

Use this Algorithm:
R T R' T'


This will bring it to the top layer then use one of the previous combinations to but it back down in the right spot. 
Goal: Move four edge pieces into the second layer, making sure that the colors on each piece match the sides where it is positioned.
Look for edge pieces that do not have a yellow sticker on them. Rotate the top of the cube, using T or T' moves, until the front sticker matches a center.
These combinations will take an edge piece from the top layer to the target position, marked with an X, without disorganizing the layer you already solved.
T R T' R' T' F' T F  T' L' T L T F T' F' 
What if the edge piece you want to place is stuck in the second layer?
Use one of previous combinations to temporarily move an edge piece from the top layer down, forcing the desired piece up to the top. Then proceed put it back down in its proper place.
Goal: Solve The Rubik's Cube after completing the last layer, which can be divided into four steps: orienting the edges, orienting the corners, positioning the corners, and positioning the edges.
Orient the edges
Have all the edges show their yellow stickers on top. There are three other possible orientations presented below, and executing this sixmove combination will cycle through these following situations in the following order.
Algorithm:
R' T' F' T F R
Orient the corners
Have all the remaining corners show their yellow stickers on top. There are seven possible positions that these corners could be in. This eightmove combination will rotate the stickers once clockwise. Repeat the combination until all yellow stickers on face up.
Algorithm:
R T R' T R T T
R' T T
Position the corner pieces
The following 13move combination, executed with yellow on top, will swap two corners as shown, and can be used any number of times in order to position all four corners correctly
Algorithm:
R' F R' B B R
F' R' B B R R T'
Position the edges pieces
This is the final step in solving the cube. You will need to position the edges in the correct locations by cycling sets of three. There are four possible permutations of the edges, and with this 12move combination, you will be able to solve them all.
Algorithm:
R R T R T R' T'
R' T' R' T R'
*Select the white side to be the top of the first layer you solve because the white stickers are easy to spot on a scrambled cube.
Jacob Benison, Information Graphic, Sarasota HeraldTribune, 15 October 2006
SOURCE: https://www.leyanlo.com/
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