By the sounds of it, you know how to extrude and push, but you get stuck on tight corners? A little trick I use with this method is, on the edge i want to move, switch to scale tool, set the pivot to object centre and turn snap on. Then highlight the vert you want to move and the vert at the other end of the edge, hold the mouse over a vert so the snap thingy comes up, then click and drag.
