The second layer is quite easy to solve. There are only two algorithms you need to learn and again, once you understand how the pieces move, one algorithm is really just a transposition of the other.
The first step is to find an edge piece in the top layer that needs to be swapped into the second layer. If you are solving the cube with the white face as the Down face, then the yellow face will be the Upper face, which means that you need to look for an edge piece in the Upper layer without a yellow sticker, this edge piece will need to be swapped into the middle layer. Next you orient the sticker of the edge piece not on the upper face, with it’s corresponding centre colour. You should then have one of the following two cases:
U R U' R' U' F' U F
The first 4 moves of this algorithm pair up the edge piece (currently in the upper layer) with the corner piece (currently in the 1st layer). The second 4 moves insert both pieces into the correct position. You should practice this algorithm over and over until it becomes second nature.
U' L' U L U F U' F'
This algorithm is really just a transposition of the first one presented. The difference here is that the edge cube needs to be moved to the left. Again the first 4 moves pair up the edge piece with the corner piece and the second 4 moves insert both pieces into place.
If you find that an edge piece is in the second layer but in an incorrect position, you should move onto another edge piece that is in the top layer. By doing this you may solve an edge piece and swap out the incorrectly position second layer edge cube.
If there are no cubes in the upper layer that need to be solved, and still some incorrectly positioned second layer edge cubes, then you need to perform one of the above two algorithms to temporarily move any edge piece into the slot containing the badly position edge cube. This will swap out the desired edge cube into the top layer from where it can be solved by using the appropriate algorithm from above.
Once you have solved all 4 edge pieces, the second layer is now complete. You can now move onto Step 3