The New York Times just released an article answering the most googled travel questions. What I took away from it is that the cheapest days to fly are Tuesdays and Fridays (when flying back in on Monday for a weekend trip. Also Google Flight Search and Hopper.com (also available as a app) can be very helpful when searching for the cheapest flights and times.
Another recent NY Times article on finding the best deals on flights recommends when booking flights to Europe the cheapest price is usually available at least six months in advance. For flights to the Caribbean, a shorter window of two to four weeks in advance will lead you to the cheapest price. Happy Traveling!