To secure the best prices on Southwest Airlines, focus your booking efforts on Tuesdays, particularly in the morning, when fare adjustments are commonly made. Check back often, as airlines frequently offer sales shortly after their weekend fares are released. 

Flying midweek—especially on Tuesdays and Wednesdays—can help you find the lowest rates due to reduced demand. Additionally, consider signing up for Southwest's Rapid Rewards program for exclusive deals and to earn points toward future flights. 
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Utilizing fare alerts can keep you updated on price changes and promotions, ensuring you never miss a deal. Lastly, be flexible with your travel plans, avoiding peak holiday periods whenever possible. This approach, combined with monitoring the website for flash sales, can lead to substantial savings and a more affordable travel experience.