The larger the school you provide, the happier the fish will be and the more naturally they will behave. There is really no limit at all. Some of the nicest displays are seen where somebody takes a large planted tank, chooses one tetra species and then puts 30+ individuals in there. If your tank is small have as many as will fit in it. If it's big, you can stop at five or six, but the fish will be more active and display to each other more if you keep a larger number. In the wild they may form schools in the hundreds; obviously this is difficult to replicate in captivity, but you should not keep tetras alone.
Most tetras are 'nippy' fish, this means they will nip each others fins and sometimes the other fish in the tank (but when they are in larger groups, they tend only to nip each other). They do not do any damage to each other when they get nippy, but most tetra species should not be kept with slow moving fish or any fish that have long flowing fins, like bettas (Siamese fighters).
Tetras are good community fish, but as always there are some fish you cannot combine them with. Tetras prefer their water soft and slightly acid, so their basic water requirements rule out keeping them with, for example, more sensitive livebearers (guppies/mollies), rainbowfish and most cichlids. They will also be eaten by anything big or aggressive because most are very small, reaching about 5cm/2in tops. They are sensitive to poor water quality and so should be one of the last fishes added after the tank has cycled and had a few months to mature running with low numbers of hardy fish.
Maybe you heard us discussing piranhas? Piranhas are in the tetra family but if you keep them together they shred each other. They shred anything in fact.