You can also do those edge-corner-edge triplets you are describing by intuition. The basic "move" goes like this:
1. You've got the corner and one edge in place. The edge to the right in this case.
2. Find the edge that goes on the left side and put it in the upper layer (face).
3. Orient that edge such that a U move will match the edge color of the edge to the center color of the front face. (The face with the edge-corner-edge triplet you are trying to form).
4. (Here comes the move) Rotate the front face clockwise two turns, which brings the corner piece to the upper left corner of the megaminx.
5. Rotate the left face clockwise one turn, bringing the corner piece to the middle left corner of the megaminx.
6. Rotate the U face clockwise one turn, matching the edge with the center color of the front face.
7. Rotate the left face anti-clockwise one turn, again bringing the corner to the upper left corner of the megaminx. Corner and two edges are now matched!
8. Rotate the front face anti-clockwise two turns, which lines up the E-C-E triplet.
There are probably other ways of doing this more efficiently (in addition to the F2L one that PJK described). But this one works, and maybe will give you some ideas to build upon.
Brian.
