Originally Posted by shapelike

Let all the air out, then squeeze out the rest of the air (every little bit will help with this). Press the sides of the tires off the sidewalls of the rims and in toward each other. Go all the way around and listen to the sickly/satisfying seal break loose. While you at it, make sure the tire bead drops down into the center groove the rim.

Now you need to really concentrate on starting at one point on the rim, pressing the tire beads hard into the drop of the rim and holding them there as you move away from the spot and further outward along the rim on either side (toward to exact opposite point on the rim). The idea here is to get yourself as much slack as possible so you can pull the tire off the rim on the other side.

PS. If you've got Continental tires save yourself the blood blisters and pick up some new levers on your lunch break.