Peter Renzland's Easy English Elegant Rubik's Cube Solution:

The Face Positions are: Up, Down, Back, Front, Left, Right.
"R" means "turn the Right face clockwise a quarter turn", etc.

1. Do the Up (white) Corners intuitively.

2. Place the Down (yellow) Corners: Turn the yellow face so that at most 2 corners are displaced. Hold them between the left thumb and index finger, and swap them: RBRB RBRB RBRB RBR. (If they are diagonal, make them adjacent for the swap.)

3. Orient the Down (yellow) Corners: If 1 yellow corner cubie is properly oriented, turn the cube so that it is Down Right Front. Otherwise turn the cube to place a cubie there, with its yellow facelet on the Right. (The White corners are always Up.) Do: RBLF RBLF RBLF. (Repeat all of step 3 until the corners are done.)

4. Do the Up (white) Edges intuitively.

5. Do the middle and Down Edges: To move an edge cubie, line it up opposite its target cubicle, properly oriented (down the Back); line up a helper edge-pair (already matched, or both still random) alongside (down the Right); Do: RRBB RRBB RRBB; invert the line-up turns (having noted their face-colours).

Keeping the centres correctly aligned may help align the corners and edges.

Intuition assistance for Step 1:
To move a white cubie from the down face into its own cubicle, properly oriented:
Hold the cube so that the target cubicle is at Up-Right-Front.
Turn the Down face to move the cubie to Down-Right-Front.
      If the cubie's White facelet is Down, do   DDD RRR DD R LLL FFF L.
      If the cubie's White facelet is Right, do   LLL FFF L.
      If the cubie's White facelet is Front, do   B R BBB.
If the cubie is on the UP face, move it to the Down face first.

See also Peter Renzland's Elegant Rubik's Cube Solution Method.

[ peter [at] dancing [dot] org ]