Heh, I could never solve the thing with my eyes open.
There's a technique. I had someone explain it to me in college, and it opened my eyes (heh) to a whole new way of approaching the problem.
Before I was focusing on the surfaces, and just moving the colored squares around on them trying to get them closer together.
But if you approach it as a three-dimensional problem, and realize that the faces on the corner blocks have to guide you to what color each side must be, then you can start to realize that there's a process involved in getting the right colored faces to the sides that they must end up on for the whole side to be the same color.
You always start with the corners...
For example:
In this one, the top corner closest to the screen shows that the top side must be white, while the right side (facing us) must be green and the left side orange.
Going to the very bottom closest corner, you're going to have to find the corner piece that fits where the right face is green and the left face is orange. There's only one piece that will fit there in that spot and make it work, so you have to find that one piece that will work and then figure out how to get it moved in that only position that will solve the puzzle.
You keep going around the corners until you get all those in place and the you can start moving to the other faces.