Your options are simple...
Repair puncture
Replace tyre
Take it to a tyre garage and ask their opinion. They will tell you if it's safe and reliable to repair it. If so, they can do it for you hopefully there and then. If not, change the tyre.
If the tyre on the opposite side of the car is still fairly new, you can get away with changing just the damaged tyre for one of the same type, if that garage sells them. If the other side is worn, replace both. It's never a good idea to have odd tyres on the same axel.... that include different amounts of tread and different models of tyre.