You have to remove the bicycle tire from the wheel rim to begin the fixing process. If the tire is relatively loose, you can use your both hands to remove it from the rim or otherwise, you might require a prying tool to do the job. Tire irons can pry and lever the tire over the wheel rim easily.
Take out the inner tire tube and pump some air into it. Find out the puncture in the tube by touching the tube all over. You can feel air coming out at the puncture spot easily. Otherwise, you can place the inflated tube in a bucket of water and see if any bubbles come out from a particular spot. Once you have spotted the hole, dry the tube with a piece of cloth.
Now comes the use of the patch kit. Take out the sandpaper or metal sander and scratch the tire tube over the punctured spot. Making the tube surface rough will allow the glue to stick to it properly.
Apply small amount of glue over the sanded area around the hole and wait for about 30 seconds to let it a bit dry.
Take a patch and press it tightly over the gluey area. Keep pressing the patch over glue for at least 30 seconds. You can even pat the patch with a metal object so that it firmly sticks to the tube.
By the time the patch and glue dry up completely, you should check the tire of your bike to see if any nail, screw or other sharp object is present within it. Run your fingers inside the tire to feel for any pointing object, glass or thorn. You need to remove that object or it will puncture your bike’s tube again.
Line the tube inside the tire and pry it over the wheel rim properly. Pump air in the tire tube as per the PSI value being indicated on the side of the tire and your bicycle is ready for a ride once again!