While the above search engines are great, they do not always include small airlines, especially in less popularly booked routes and/or in remote regions. If you're flying somewhere obscure, Google search and ask around if there exists a local airline. While in South America we learnt that the LADE Air in Argentina (run by the military) has cheap flights to Patagonia, which is of course not listed in mass search engines online.
Visit individual airlines’ websites. Although airfare search engines are great, what they don’t tell you is that some airlines reserve their best deals for people who visit their sites specifically. Search for a list of large and local carriers in your area, and then search each of their sites specifically for the best deals. When coupons, discounts, or sales are offered, they will typically only be advertised on each specific carrier’s site and will run for only 1-3 days.
While many theories exist around booking specifically on a Tuesday to save money, the reality is there is no consistent truth to exactly which days are cheapest to fly. Most of the time it is cheaper to leave on a weekday, though this isn't always the case. Your best strategy is to get a quick visual of prices for a whole month to see what days are cheapest for your specific route. Here's how: