Flat tyres are a fact of life when bicycling. Most bicycle tyres use inner tubes to keep the tire round and functional. Holes and punctures happen when the inner tube is compromised. To repair the tyre flat, fix the inner tube puncture. Carry a small inner tube patch kit to fix these pesky flats when riding.
Remove the wheel with the flat tyre from the bicycle. Most bicycles use quick-release levers to accomplish this. Push the quick-release lever down, and grip the brakes and pull the brake housing out to release the brake and pull the wheel out from the frame.
Unscrew the tube cap and slide one of the tire levers between the rim and the tire edge. Slide the lever around the exterior of the rim - the lip that houses the tyre itself. This dislodges the tire from the rim, allowing you to remove the inner tube. Pull the tube out from the tyre.
Grip and apply pressure to the inner tube going around in a circle. Force pressure on the tube like you apply to a toothpaste tube. Hold the inner tube to your ear as you force this pressure on the tube and listen for the leak. After you hear the leak, isolate the puncture section of the tube.
Sand the puncture area with the sandpaper from the patch kit. This makes the rubber rough so the glue has more pores to set into with the patch. Take one of the rubber patches from the kit and apply the adhesive from the kit to the back of the patch. Press the patch to the puncture area.
Hold the patch on the tube for five minutes to set the glue. Let the glue dry for at least 10 minutes. Grip the inside of the tyre while the glue is drying and run your fingers around the inside of the tyre to feel for any sharp rocks, glass shards or thorns that might have punctured the inner tube and remove them.
Spread baby powder around the inside of the tyre to make pushing the inner tube back into the tire easier. Push the inner tube into the tyre and align the air valve to the nozzle hole on the rim. Push the nozzle into the rim air hole and push the tyre back onto the inside edge of the rim. Pump the inner tube back up, place the wheel back on the bicycle and continue your ride.