My daughter Morgan learned how to solve a Rubix cube and taught me. Thanks Morgan! However, her notes were unreadable to me so I had to create my own notes on the steps.
Here they are:
Note: The syntax of the Rubix cube movements used in this doc are as referenced from the "front" face of the Rubix cube. So even if you have to twist the cube around during a sequence always remember that the next instruction is relative to the original front face. Also "R" is the front face right column, "L" is the front face left column, "T" is the top face, "B" is the bottom face, "c" is clockwise relative to either the front face or the top face (looking down on it), "cc" is counter-clockwise relative to either the front face or the top face (looking down on it).
1. Pick a color for the "top". Make a cross on that color with the middle edges aligning with their respective side color middle pieces.
2. Find the corner piece that, given the correct alignment, will fill in the corner piece of the top color. Without messing up the top cross align that piece to be in the front bottom right corner. Use Rd-Bc-Ru-Bcc over and over until the piece in question is in the correct spot and in the correct alignment.
3. Repeat Step 2 for each of the top corner pieces.
4. Once the "top" color is done the top line of the sides should also be done. At this point flip Rubix cube top to bottom. (i.e. Put the "top" on the bottom now.)
5. The next step is to fill in the side middle lines. Locate on the new "top" side a middle edge piece that doesn't have any of the top color in it. (i.e. Its colors should be colors of the sides NOT any color of the top or bottom sides.)
6. Rotate the top such that this middle edge piece's side color aligns with the middle color of the side. (Make this the "front" for now.)
7. Look at the "top" color of this piece. The associated middle side piece color will be on the left or right of the front. Depending on which side will depend on which step you take next.
8. If the "top" color of this piece is on the right then do: Tc-Ru-Tcc-Rd-Tcc-Fcc-Tc-Fc.
9. If the "top" color of this piece is on the left then do: Tcc-Lu-Tc-Ld-Tc-Fc-Tcc-Fcc.
10. Once the side colors have their bottom 2 rows done it is time to make a cross of the top color on top. Use Fc-Ru-Tc-Rd-Tcc-Fcc to make the cross with the side colors aligning with their respective side middle color.
11. Now to find the side middle verticals. Use Ru-Tc-Rd-Tc-Ru-Tc-Tc-Rd. NOTE: You may need to rotate the top to see if the middle verticals are correct.
12. Use Tc-Ru-Tcc-Lu-Tc-Rd-Tcc-Ld to put the final corner pieces in the right place but maybe not the correct alignment.
13. Finally use Rd-Bc-Ru-Bcc to put the front top right piece in the correct alignment. THEN rotate the top clockwise and do the front top right corner piece. DO NOT change what side is front during this step or you'll have to start all over. The Rubix cube will look mixed up until you get totally done.
14. Marvel at the fact you can do this!