Shift the chain to the smallest rear cog, if you're changing the rear tire. For either wheel, loosen the skewer running through the center of the axle.
Unhook the brake cable from the boot. This is the portion of the cable that first enters the brake caliper. Unhooking the cable will force the brake shoes to open wide, giving the wheel enough clearance to be removed from the bike. Remove the wheel now.
Release any remaining air from the tire. Working opposite the valve stem, insert the tip of a tire lever beneath the tire bead. Attach the opposite, hooked end of the lever to a parallel spoke. Do the same with a second tire lever, working a few inches to the right or left of the first lever.
Insert a third lever beneath the tire bead. Do not attach the hooked end. Instead, rotate the lever around the circumference of the tire, freeing the bead from the rim.
Remove the inner tube. Carefully pull it free of the tire until you come to the valve stem. Remove the valve stem portion of the inner tube last.
Free the other bead from the rim. This will be much easier than the first bead and requires no special tools.
Fit the bead of one side of the new tire onto the rim. Be sure the tire label will be located on the right, drive-side of your bicycle. Also, the label information should be aligned with the valve stem hole on the rim.
Partially inflate your inner tube to give it a little shape. Insert the tube valve stem into the valve stem hole on the rim. Work the tube carefully into the tire. Ensure that there is no tube caught between the rim and the tire bead. This will almost certainly cause a flat!
Hold the tire in your lap or on a work surface, and, using your thumbs, push the second bead into the rim. Use your hands to roll the last section into place. Avoid using your tire levers if possible, as they can puncture your inner tube during this procedure.
Insert the tire back onto the bicycle. Tighten the skewer and reattach the brake cable to the boot on the brake arm. Inflate the tire to the recommended pressure.