There are classical guitarists who don't use their fingernails, keeping them trimmed ultrashort, but I prefer the sound that comes from the mix of nail and flesh.
You can get a nail salon to glue some on for you, do silk wraps and what not, but those are a little harder to deal with, getting, and removing them. Better for steel string players, since they last longer.
Fortunately, I have a little emergency repair kit, based on one I once bought online. I can't seem to find that kit for sale any more, but it's easy to cobble one together from stuff you can get at the drugstore. (Editor's note: I sit corrected -- I found 'em: Riconails, here.)
It's only a temporary fix, but they'll generally stay on long enough for a good session, which is all you need.
Basically, you get some plastic or nylon nails, trim them short to fit, and stick them to your own nails using Glue Dots™. If you don't know what these are, they are essentially flat little circles of gummy stuff, kind of like preformed disks of rubber cement on a roll of paper tape, and conveniently about the size of a fingernail.
You peel one off the backing paper, lay it on your nail, then press the artificial fingernail firmly into place. Unlike super glue, which is full of vile chemicals that can leach into your keratin and weaken it, as well as causing cancer, hair loss, and exploding testicles, the glue dots are harmless, temporary, and can be easily rolled up and off using an orange stick when you are done. The nails are reusable.
Back in the day, classical guitarists would repair their nails with glue and tissue paper or ping-pong balls. There's nothing quite like your own nails, but other things can be made to serve.
