Step One: Solve the top third. If you can't figure this out on your own, then stop here.
Step Two: Solve the middle third. The following sequence transfers an edge piece from the bottom-left to the front-right, and leave the top third in the same state that it began:
(right side counterclockwise) (bottom side counterclockwise) (right side clockwise) (bottom side clockwise) (front side clockwise) (bottom side clockwise) (front side counterclockwise)
Call this sequence 2A.
Here is X's mirror image about the front-right to back-left diagonal plane:
(front side clockwise) (bottom side clockwise) (front side counterclockwise) (bottom side counterclockwise) (right side counterclockwise) (bottom side counterclockwise) (right side clockwise)
Call this sequence 2B.
Perform these sequences. Repeatedly. Learn exactly what they do.
Step Three: Position and orient the bottom edges. (2A + 2

will rotate and flip three of the four bottom edges. Call this 3. (Note that the last move of 2A is cancelled by the first move of 2B, so you can collapse the sequence a bit.)
As above, study 3.
Step Four: Position the bottom corners.
New sub-sequence: 2X = 2A + (bottom side clockwise)
(2X + 2X + 2X + 2X) will rotate three of the four bottom corners. Call this 4.
As above, study 4.
Step Five: Orient the bottom corners.
(2A + 2A + 2A + 2A) will alter the orientation of three of the four bottom corners. Call this 5.
As above, study 5.