Solution #1 (Step 2)

Step 2 -- Do the middle layer edge pieces

Okay, so the U face is done...Now we have to get the edge pieces of the middle layer in place, that is the FR, FL, BR, BL pieces.

There are four possibilities:

• Edge piece is in the correct place and oriented correctly -- do nothing.
• Edge piece is in correct place, but oriented incorrectly. In this case, you have to replace it with another piece temporarily. Choose an edge piece that is on the D face, and move it to the position of the aforementioned edge piece using the move described in the following list item.
• Edge piece is in an incorrect place in the middle layer. In most cases, you can just skip this edge piece for now, as it will move to the D face when you put the correct edge piece in that place. If you have two edge pieces in the middle layer that are in each other's correct places, then you will need to break the cycle by replacing one of those edge pieces with one of the D face edge pieces.
• Edge piece is on the D face. This is good. Let's say you want to move the yellow-red edge piece into place on the middle layer. (Your cube may not have yellow and red as adjacent pieces, so you may have to substitute different colors). Check which side of the yellow-red piece is actually on the D face. Say yellow is on the D face. Rotate the D face so that the yellow-red piece is opposite from the yellow center. (If the yellow center is on the F face, then the yellow-red piece is the DB piece, got it?). Now, hold the cube so that white is the U face, and the yellow center is on the F face. Which side of the yellow-red piece is the red face on? If the red center is on the L face, then apply F' D' F D L D L'. If the red center is on the R face, then apply F D F' D' R' D' R. One way to think about this move, if you're trying to memorize it, is that you are removing the corner piece on the U side right above the edge piece you're trying to replace, and then putting it back in from the other direction, with the side effect of moving the edge piece into the correct place.
  

This will have to be repeated at least 4 times in order to get all of the 4 middle layer edge pieces into place.