There are a few ways. Some that friends and I have tried:
Note: obviously, the best thing to do is see the dentist and have it taken care of, however, most aren't open on Saturday, sooo:
ibuprofin for swelling, tylenol targets tooth pain best in my experience. (I'm not a medical professional by any means, so please be aware of what you can and can't take)
cloves on the infected area.
you can find numbing medicines at the store
a lot of people use strong liquor. (if they are of legal drinking age)
I personally use pure mint or almond extract. Let it set for a moment. It numbs everything. Do NOT swallow. It will make you sick. Also, it's about 90% alcohol, so you will fail any breath test.