I assume the puncture is in the tube ! Sometimes it is worth checking te valve first to see if air is slowly escaping. A little spittle on the top of your finger is still the best... ok... no well..not here.
1. Turn cycle upside down and leaver off one side of the tyre with one/two tyre leavers (or old fork handles). If the problem is with the back wheel, leaver off on the opposite side to the chain.
2.Slip out the tube on this side starting at the valve and then out add some air to the tube to identify where the air leak is.
3. Having found the leak, clean the area around the hole with sandpaper from the "tyre repair kit" and spread a light film of solution (with finger tip) over the area and allow to dry to the touch. (1to3 mins.) Center the patch over the hole and press firmly with thumbs.
5.Chalk over any excess solution around the patch to prevent tube sticking to inside of tyre.
Add more air to check for other leaks (you can immerse tube in water to check for any small leaks if necessary) Release all the air .
Reverse the process of putting the tube back starting at the tube valve.
Happy Cycling
john o, June 2008