After the corners are solved, use the instructions for the 3-color cube to solve the edges. Restore the corners with half-twists and then use the following sequences to complete the solution. You may not always be able to exactly match a setup but you can always find one that will either reduce the number of misplaced facelets (matching 3 of 4 facelets will fix two) or relocate two of them such that a setup can be matched. Some additional tips for solving the Edge Cube are here.

All configs in this stage are solvable with half-twists including E2 & E4 above which also use quarter-twists to reduce the number of moves to solve. In this computer-generated list of half-twist only solutions for every possible config it can be seen that E2 (154) takes 12 moves and E4 (13) takes 8 moves (note: the configs are rotated into a different position).

A quick reference guide for all of the solving sequences is here.