How to patch a tube
First you need to find the hole. Inflating the tube with a pump will cause it to expand making the hole easy to find by listening for escaping air. Alternatively you can submerge the tube in water and watch for bubbles. Mark the hole with a pen or a crayon (sometimes provided in a patch kit).
If you submerged the tube dry it first. Prepare the tube by roughing up the area surrounding the hole with emery paper* taking care to remove any raised edges. If possible wipe the area with a solvent so it is totally clean.
*Emery paper is a type of sandpaper.
Apply a layer of glue the size of the patch. Keep the layer of glue thin and consistent.
Let the glue dry for a few minutes. It will turn from shiny to dull when it’s ready for the patch.
Apply the patch over glue and push down firmly for a couple of minutes then leave it to dry.
After 10 minutes remove the backing from the patch. The backing will start to blister making it easier to remove. Avoid pulling up the edges of the patch.
Finally apply some talc or chalk (sometimes provided in a patch kit). This will prevent the patch from sticking to the tyre.