Remove wheel, let the air out and replace the wheel on the ground, sprocket up.
Break the tire bead away from the rim by pushing down on the sidewall with your hand or foot.
Flip the wheel over and break the other bead (the majority of the work will be done with the wheel in this position: sprocket down).
A couple of other big tips:
First, use a good pair of tire irons.
Second, spray or rub the newly exposed beads with slightly soapy water solution.
Use your irons to begin working the tire off, starting and then finishing near the valve stem like this:
Take the spoon end of both irons and insert them into the tire about four inches apart, spoon up and under the bead, one on each side of the valve stem. Now (this is critical) place your knees on the sidewall on the opposite side of the wheel from your irons, forcing the bead into the well of the rim (where the hidden ends of the spoke nipples are). Always keeping the bead in this center section opposite from where you're working will make a world of difference in changing a tire.
Now pull back on the irons, lifting the bead over the edge of the rim. Remove one tire iron or use a third one, and take another bead (usually where it's just starting to come out of the rim), forcing the iron between the bead and the rim, lifting up and repeating the process all the way around until the entire bead is out. Remove the inner tube.
Stand the wheel up and remove the second bead by sliding the iron under the bead and over the rim, then lift up and come over the top, forcing the tire down with both your iron and your free hand. You may need to take another bite with your iron, but often times it will pop off at this point.
