Today I have decided to take a quick look at some aspects of archaic language. I see people mix these up all the time, and it comes down to a lack of understanding of the grammar.
Thou is nominative (subject form), thee is object form, and thy/thine is possessive form.
The use of thy/thine depends on the object of which you are speaking. A good general rule is that thine goes before words beginning with an h or a vowel. The same holds true if you are choosing between my and mine.
Here are some examples:
Thou art a fool.
All my foolishness I give to thee.
Thy foolishness offends me.
Thine eyes are full of mischief.
And here is a quick glossary of some other archaic terms you may come across in both historical works and historical fiction.
Henceforth: from now onwards
Hither: to/towards this place
Hitherto: until now
Thither: to that place
N.B. Many modern readers seem to misunderstand Juliet's balcony scene. When she asks 'Wherefore art thou Romeo?' she wants to know why he has to be Romeo, her enemy. She's not asking where he is. :)