The tire should be fine if it still has tread, the bead seats all around, and it doesn't have any very large cuts that go all the way through.
When you take the tire off, run your fingers all around the inside of the tire to make sure there's nothing sticking through. Use whatever you need to dig it out (pliers, pick, small screwdriver) - as long as you don't make the hole huge, it will be fine. Also check your rim strip and make sure there are no sharp edges poking through there - if there are, replace the rim strip.
If it's a puncture and not a bad valve, patch the tube. Most people have (at least) two tubes, so you can put a good one in when you need it, and patch the bad one at your leisure. Rubber cement type patches tend to be more reliable than the self-stick ones.