Remove the wheel from the bicycle and the tire and inner tube from the rim, following the steps in How to Change a Bicycle Tire, “Removing the old tire.”
Inspect the inner tube for holes by inflating it with a bicycle-tire pump until you can hear air escaping. Many holes are not visible until the tube is highly pressurized.
Locate the hole. Hold the tube close to your cheek and feel for escaping air if necessary (see picture). Lightly rough up the area around the hole with sandpaper.
Check the tire to fine the source of the puncture by running your fingers around the inside of the tire. Be careful, sharp objects may be imbedded in the tire. Visually inspect the outside of the tire for rips, tears or sharp objects. Be sure to remove the offending object so you don't get another flat!
If you plan on riding a lot, carry a pump and a patch kit, and even replacement inner tubes, on your bicycle at all times.