Remove the tire and tube: Remove the valve cap and nut (sometimes found on Presta valves: inset photo). For Presta valves, unscrew the tip (inset photo) and press down to let all the air out. For Schraders, poke the end of your tire lever into the valve to release all the air. Starting directly opposite the valve, wiggle a tire lever beneath the tire's edge and pry down to lift. If possible, hook the lever on a spoke (many levers are made to do this), or hold it in place. Place another lever about 6 inches away from the first and pry here (main photo). Continue with your third lever until you can get one side of the tire off. Then reach inside and extract the tube. Pull the other side of the tire off the rim or pry it off with your levers.
Tip
If you have trouble getting the tire off, make sure all the air is out of it. Even a little air can make the tire a lot tighter.
Some cyclists prefer to remove only one side of the tire to ease reinstallation. The disadvantage is that it's harder to check inside the tire to find whatever popped the tube.