I do it by finishing 1 side, leaving 1 corner '
unsolved'. This gives you a lot of
freedom, since if the solved side is on the bottom, and the
missing corner is in the
bottom right, you can turn the front and right sides. This makes finishing the middle slice fairly
easy, again leaving the edge piece above the
space unsolved. You then make a T on the top face, leaving 1 edge piece on the top unfinished. If the unsolved piece is at the bottom/back/right, then the unsolved piece is the top /middle/right. You then fix the last 2 edge pieces, position the corners
correctly, then rotate the corners, 2 at a time, one clockwise and one anticlockwise.
There are 43,252,003,274,489,856,000 solvable positions the cube can be in. If you had 1 cube for every position they would cover the surface of the earth 250 times.