The Face Positions are:
"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 layer 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 exactly 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).
Keep the centres correctly aligned throughout. This helps align the corners and edges sanely.
[ peter [at] dancing [dot] org ]