Like dsbrantjr said, if the cords in the tire casing are cut, it's irreparable. Last year, I ran over something that cut the cords on a brand new tire. Only had about 10 miles on it. Grr...

You can "boot" the tire as a temporary fix. (How temporary? Depends on how lucky you're feeling.) A tire boot is basically something that resists stretching, applied to the inside of the tire itself, to provide structural support where the tire's cords are cut. Park Tool sells tire boots. I use scraps of kevlar fabric from drum heads (my other hobby). Tyvek mailing envelopes are reported to work well. Dollar bills work well enough in a pinch if you need to improvise a roadside repair to limp home.