When you have one side on and you run into tight spots on the other side, just stick the flat end of the lever underneath the bead (so between the tire and the rim). Then lever it up using the rim as a pivot. As you lift up the other end of the lever (the end not resting on the rim) it'll lift the bead up and over the rim.
It's pretty simple although difficult to explain clearly. It's pretty much just doing the removal procedure in reverse. Be careful not to snag and tear the tube in the process