With most airlines, you have to call and ask for their military fare. Very few airlines offer a straight-forward discount. A good example of a straight-forward discount is JetBlue. Whatever is the lowest fare you find online on their website, call their 800# and they will offer you 5% off. What a great deal!
What we can't recommend here at GuidetoMilitaryTravel.com, is Veterans Advantage. You will see that some airline websites redirect you to that site. It is is paid membership we don't know much about so we can't recommend it. I've always been a big believer that the military shouldn't have to pay to access discounts that are rightfully theirs. As we find out more about the program, we will let you know. Meanwhile, there are other options for discounted airfare that don't require membership.
Here are some links to the different webpages with airline discount information.
Southwest Airlines: Southwest does offer a military discount. It's not necessarily the lowest fare but it does offer a must lower fare on last minute purchases when available. If you have little time to plan and are trying to purchase airfare with less than a 21 day in advance notice, the Southwest Military discount would probably be the best bet. You have to contact them personally for more information or to compare rates. Call 800-IFLYSWA.