Notice there is no “e” in one of the words.
Also, the “e” is in a different place in the other two words.
Rule: Quit has no “e”, therefore the “i” is a “short i“.
So the “i” in quit sounds like the “i” in pit.
Meaning: Quit = Stop
Quiet. If you sound it out by carefully looking at the letters, you find it is the only one of these words that has two syllables. Qui-et. 
Quite is another way of saying very. For example, the sky is quite bright today.
Since there is an “e” on the end, the “i” in quite is a “long i”.
So the “i” in quite sounds like the “i” in kite.