Every once in a while a writer takes it into his head to express himself in archaic language for humorous effect, or—more legitimately—for the sake of verisimilitude in historical fiction. As for the humorous effect, it is probably never as humorous as the writer thinks it is, but that is not the Editor’s concern right now.
His concern is that both the humor and the verisimilitude work best if you actually get the language right. Since the archaism is usually limited to sprinkling “thou” and “thee” around and using a few older verb endings, the principles of getting the language right are easy to understand. All you need to know is what the pronouns are and how to conjugate a verb the Early Modern English way.
In pronouns, the only serious difference is in the second person. For the singular, we use thou, thee, thy, and thine, which work just the same way I, me, my, and mine work in the first person. For the plural, ye is often used as a subject rather than you.
Note in particular that thou and thee are always singular. You never use them to refer to more than one person. So when, for example, God tells you “Thou shalt not covet,” he is looking you straight in the eye and speaking to you personally.
Now the verbs. Let’s start with a standard regular verb, like “start.”
First Person: I start
Second Person: Thou startest
Third Person: He, she, it starteth
First Person: We start
Second Person: Ye (or you) start
Third Person: They start
The only differences from modern usage are in the endings for the second and third person singular. For some reason, even writers who are attempting verisimilitude (rather than sarcasm) often get those mixed up. Just remember that -st is always the mark of the second-person singular: that is, it always goes with thou.
The past is the same as it is today, except in the second-person singular, where the ending -st is persistent. Usually we make the second-person singular past with the auxiliary verb “didst.” “Thou startedst” is correct, but “thou didst start” is far more common.
Many verbs are irregular, of course. With few exceptions, they have not changed in the other persons, so all you need to know is the second-person singular form.
Present: Thou art
Past: Thou wast
Present: Thou mayest (or mayst)
Past: Thou mightst (or mightest)
Note both the second-person and third-person singular of to have: thou hast, she hath. The second-person-singular past is thou hadst, or, in even older English, thou haddest.
Similarly, to do: thou dost, she doth, thou didst.
Finally, if you are attempting serious verisimilitude, you might want to note that there is no possessive pronoun its in very early Modern English. His is used instead: “The sun hath run his course.”