Take the new die face. Insert the *corner* of the new face under the middle of the *edge* of the old face, and lever it up a bit. Then do the same with a second edge. Move on to the third edge and do the same. The face will pop off after the second, third or fourth edge. It takes just a few moments. It works best if you hold the die flat on the table; I found that it was less precise if I tried to hold the die in my hand instead.
They jump up like crazy. First game, they were flying meter high above the table, when we've tried to remove them. I've found that it's best to lift one edge and then an edge directly adjacent to it, not the opposite one. After two, it usually comes off.