Algorithms for the first two layers

After you built the cross of edges on the first layer, you need to build up two solved layers of the cube. See animation below.

Depending on your own preferences, you can keep the cross on top, on the bottom, on the left, or even on the right.
Most top class cubists keep the cross at the bottom or at the left, because you can use many R and U moves and have a good overview of the cubies.
I dissuade you from keeping the cross at the front or back, because then you do not have a good view of the cubies you want to solve.

For people who keep the cross at the left
First two layers algorithms All algorithms you need to solve the first two layers, after making a cross on the first layer.
First two layers algorithms, printable page See previous link, but now in small format, to print on only one page.
 
For people who keep the cross at the bottom
First two layers algorithms All algorithms you need to solve the first two layers, after making a cross on the first layer.
First two layers algorithms, printable page See previous link, but now in small format, to print on only one page.
 
For people who keep the cross at the top
First two layers algorithms All algorithms you need to solve the first two layers, after making a cross on the first layer.
First two layers algorithms, printable page See previous link, but now in small format, to print on only one page.
 
Other F2L tricks
Advanced tricks for F2L Advanced tricks for solving the corner/edge pairs of F2L.