These two videos will get you on your way to using the Fridrich F2L Method to solve the Rubik's Cube. What is F2L? The first two layers, of course.
You'll see in this tutorial how the F2L in the Jessica Fridrich Method works, so that you will never have to learn the algorithms for it. The method explained here is foolproof, meaning that it works every time on the Rubiks Cube, but takes a little longer. Placing one corner-edge pair should not take more than about 7 or 8 moves. If a move is taking you longer, it's probably a good idea to learn the algorithm for it. This is however quite rare, so you don't have to worry about it unless you want to go for 20 seconds or so.