From David Fiedler,
Your Guide to Bicycling.
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Patching a tube that has a hole in it should allow you to keep riding if you get a flat and aren’t carrying a spare. Everything you need to patch a tire is available in an inexpensive patch kit that I highly encourage you to carry at all times.

These steps assume that you’ve already removed the tube from the tire. If you haven’t done that yet, follow this link to get directions.

If you are cost-conscious, patching your tubes and using them again may be an option to try and save some bucks, but be forewarned: a patched tube will never be as reliable as a new one. The patch can fail again, so to be on the safe side, a patched tube should probably be replaced with a new one as soon as you get the chance.