You can get the best prices if you book at least 6-8 weeks in advance for domestic flights and 2-3 months in advance for international flights.
Flights on Tuesdays and Wednesdays are generally cheaper, as there is less demand on these days. Avoid weekends and holidays to get the best flight deals.
In many cases, booking a round-trip with the airline can be much cheaper than buying your one-way ticket. You should try to compare the prices of both options to get the best deal.
Airlines publish the cheapest tickets early in the morning or late at night. This can increase your chances of finding cheap flights.