Promptly get the bike off the road once the tire pops. Get to a safe location, turn the bike upside down to inspect the flat by looking to see where the hole is. If you immediate identify the puncture, use the patch kit to fix the hole. If you cannot find the puncture, remove the tire from the wheel.
Insert the end of a plastic lever inside the lip of the tire. Slide the lever to the left so you can pull the lip over the rim and all the way around the tire.
Use two levers under the lip of the tire if the tire keeps popping back into the groove. Hook the tail of the first lever around a spoke while you use the second lever to pull the tire lip over the rim.
Use sandpaper, between 200 and 400 grit, to scuff the area around the puncture. According to Bicycling Life, scuff around the puncture, making the scuff mark larger than the patch you will apply. Spread a thin layer of the glue that came with the patch kit to the puncture, just enough to dampen the surface. Allow the glue to dry five minutes.
Peel the plastic from a patch, sticking its adhesive side on top of the glue. Press down on the patch with your thumb for 60 seconds. The harder you press on the patch, the better it will hold.
Place the valve in the rim's valve hole and work the tube back into the tire. Tuck the tube into the tire all the way around the rim. Correct any twisting so that the tube is distributed evenly around the tire.
Replace the tire back on its rim. Put one side of the tire one the rim and work the rest of the tire tube all the way around the rim.
Re-inflate the tire. With a mechanical or manual air pump, pump enough air back into the tire so that it stands firm.