Sometimes especially when I am reading books or quotes, I encounter verbs ending in -th. Is that an arcaic form? How should I properly translate them?
Verbs ending in -eth are an archaic way of forming the 3rd person singular present, so for example:
sayeth => says
goeth => goes
Beyond that, I can't think of any verbs ending in -th that don't end in -eth. As J.R. points out in the comments, doth doesn't end in -eth. It is, however, still in the 3rd person singular present (i.e. equivalent to does), and I would hypothesize it comes from assimilation of doeth. In any case, it's probably safe to assume that all verbs ending in -th are in the 3rd person singular present.
How should I properly translate them?
That depends on the nature of your translation.
If you are only trying to convey the sentiment of the statement, then I would simply figure out which verb is being used, and conjugate it in its modern form. So Aristotle's:
He who hath many friends hath none.
Can be rephrased as:
He who has many friends has none.
But that's not really a "translation," that's a modernized paraphrase.
This all hinges, then, on which language you are translating the English into, and whether or not that language has some mechanism to preserve the archaic "feel" of the original – if it's even the "original."
One important fact to keep in mind is whether or not such archaic language was part of the original. For example, Aristotle's quote was probably translated from Greek, so either of the versions I mentioned earlier would be valid. Also, earlier English versions of the Bible mention "Thy rod and thy staff" in Psalm 23, but that text was originally written in Hebrew, not English, so the word thy in that instance is part of an early translation, not necessarily part of the original text. Such words found in Chaucer or Shakespeare, though, would be part of the original.