You use thee like you'd use "tu" in French: when you're speaking to one person who is either your close friend or lower in social hierarchy than you. Maybe between equals too, to be honest I'm not that sure. So you'd say thou to your family members, friends, children, servants, slaves and enemies. Anyone you wouldn't normally be polite towards. But only if there's only one of them. If there are more, it's "you" again.

Thou fell out of use simply because English speakers were too polite to use it with anyone anymore, so eventually people just forgot about it. xD So if you ever wanted proof that the English are too polite...