From experience:
Get a puncture repair kit, use levers to take out innertube, pump it up and listen for hissing (if you cant figure it out use a bowl of water to see the bubbles leak), use the yellow crayon in the kit to circle the puncture, deflate innertube, rough up the rubber surrounding the hole with the sand paper, put vulcanising solution around (bit wider than the included patch size) and leave to go tacky, put patch on vulcanising area (red side down), hold down for a few mins, grind up chalk and sprinkle over and around patch to dry out area in question (makes sure vulcanising solution doesnt stick to tyre when put back in), check tyre for glass/metal/debris and remove all, pump inner tube a little and put back into tyre (avoids snake bites), lever back onto rim.
Done.
Takes 2-3 mins.
No need to take wheel off or anything.