Put the four middle-row edge pieces in the correct. Spin the bottom layer until the corner is directly under the piece it needs to replace. If you want to further understand the cube and not rely on any memorized algorithms at all, you should take a look at this post on solving general permutation puzzles, which includes a section on the 3×3×3 cube. Put the top corners in their correct positions and orientations. White pieces at the bottom take an extra step.

Solve the last corner-edge pair in any way you want.

Can you do it Cube with a yellow middle and 4 white sides surrounding it. You see, you can rotate the bottom layer to align that unsolved corner with any middle layer edge position and then easily chuck the edge piece in (because you do not care about messing up the unsolved corner). Your goal is to get four white pieces around the yellow piece in the center. I highly suggest learning this before going into M2. If you are lucky youll move some of the incorrect. Turn the puzzle to the side, or even right around, so that the pieces you want. You just need to turn the top-layer and/or the whole cube (keeping. Its easiest to start with any pieces which are on the top layer and then deal with the other pieces next.

Use the unsolved bottom corner to facilitate solving 3 of the middle layer edges. You set up corners to a receiving spot and swap it with the bank piece. As you can notice the corner sequence swaps the top-right-front and top-right-back corners.

Solve only 3 corners on the bottom layer.

Since it seems that you are not looking for just memory work (otherwise you should just memorize all the F2L pair algorithms), I recommend you instead solve F2L as follows:

However, it is clearly troublesome otherwise. As someone commented, F2 U2 F2 U2 F2 works if the edges in question are oriented suitably. The standard F2L pair algorithms cover all cases, but if you want intuitive rather than fast solution then actually you should not solve layer by layer.

Rubiks cube flip a side piece