1. Find the cheapest day to fly, best if you have flexibility in your schedule: how to do this? Go to a flight search engine that shows you a calendar or overview that shows you what flights cost on different dates. Some good search engines for this are kiwi.com or googleflights.com.
2. Collect flight points with credit cards. Even if you are not using that card to purchase flights, you are still receiving points on other purchases which will come in handy later when booking those flights! For internal USA flights, my favorite credit card is Alaska.com. You not only receive 1 point per dollar, you get more points when you purchase flights with them and their customer service is great!
3. Sign up for flight providers and newsletters. You will be one of the first to get notified by your favorite airlines about deals and savings. In-flight search engines, you can also set up a price alert for your search; so you will get notified by email about when the best purchasing dates are.
4. Pack light and book ASAP! It always helps to book a flight in advance and not wait till the last minute. Cheap airlines such as RyanAir typically sell out of their cheapest tickets first, and the ones left closer to the date are the most expensive. So travel light to avoid check-in baggage fees and overpriced last-minute airline tickets.