Why am I saying it here and now, because I have re-read my printed books after I had clicked 'publish', and yes this is after I had received the books in the post and read them through before doing so, and months after publishing I still see mistakes I should have picked up on before putting it out to the public.
LETTING IT REST will allow you to come back to it and read it as if you are the reader, not the writer, and iron out those little things you weren't able to see because you were too close to it so soon after writing the idea on pages.
What do you do whilst you are LETTING IT REST? Write something else. This will allow your mind to become so engrossed in a new story, you will forget about the previous one and every word you used in it. Ergo, when you do go back to it you will read every word anew and know every word is in its rightful place.
How long do you LET IT REST? As long as it takes to forget about it. If for example you have written a novel of 90,000 words, write a few short stories, or at least three good length chapters of another book. This really depends how long it takes you to forget what you've been working on. Experiment until you find the answer.