The Second Layer
Now that we have the white face completed and the center pieces of the second layer in place all we need to do to complete the second layer is place the second layer edge pieces. This turns out to be relatively easy.
This step is essentially just a single algorithm and its corresponding mirror image.
Just like in the previous step we will rotate the cube so that the second layer edge we want to place is on the face facing us. Next we will line up the piece we want to place there on the top layer also facing us. Then it is a matter of slotting it in by either moving it down and left or down and right by using the following algorithms.
Now you might be asking "but what if that piece was the other way around? (ie. with the orange panel on top)" That's ok. All we need to do is rotate the cube so that the blue face is pointing towards us, line up the piece with the blue face then perform the mirrow image of the algorithm to slot it in down and to the left like so.
Some of the pieces we want to place will be in the top layer but most likely some of them will also be in the second layer (but in the wrong place or in the right place but wrong orientation). It's easiest to start with any pieces which are on the top layer and then deal with the other pieces next. If you are lucky you'll move some of the incorrect second layer pieces up to the top layer in the process and save yourself some time.
When you get stuck however you may use the same algorithms as above to put another piece into the place where the piece is you want to get to the top layer. That will also move the piece on the second layer up to the top layer. In the example below we want to get the red/green edge out of the second layer to the top layer.
For extra flexibility, once you are comfortable with these algorithms, see if you can apply them to the face pointing away from you without rotating the cube. This can save you valuable time.