This is what was given me, and from what I gather - the simplest way to put it is - use THOU when you are speaking TO a person - and THEE when you are speaking ABOUT a person. But then there's the verb changes... Have fun!
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When using the Second Person Familiar form of address.... Thou Shalt use "thou" when it is in the subject of the sentence, and "thee" when it is appears anywhere else in the sentence. For example: Thou art a varlet ("Thou" being the subject), I think little of thee ("thee" not being the subject but the object).

When using the Second Person Familiar form of address... Thou shalt change the verb by adding an "est" ending when the subject of a sentence is "thou". For example: Thou runnest. Thou sleepest. Thou speakest.

When Second Person Familiar (Thou) is used, the "est" verb endings are used in EVERY tense. Examples:
Present tense: Thou runnest
Past tense: Thou rannest
Future tense: Thou shalt/wilt run


When using the Third Person form of address (pronouns) ... Thou shalt change the verb by adding an "eth" ending when the Third Person ("He/She/They, It" is the subject. Examples being:
He/She/They/It runneth, He/She/They/It sleepeth, He/She/They/It speaketh.

When the Third Person form of address is used in a past or future tense sentence, do NOT get jiggy with the verb endings. Examples being in this case:
Present tense: He runneth
Past tense: He ran
Future tense: He shall/will run

Thou shalt also on occasion drop an Auxillary Verb in front of the verb, and give "it" (the auxillary verb) the funny ending instead of the main verb, as in dost for Second Person Familiar (Thou) and doth for Third Person (He/She/They/It). Examples:
Thou dost protest too much instead of Thou protestest too much.
Or
He doth protest too much instead of He protesteth too much.