1-Joint warfare. Working effectively with the other services is very important. The air force got a dose of this in late 2001, when the invasion of Afghanistan was ordered. With no nearby airbases, the navy carriers were the major source of air power early on. U.S. Air Force tankers were needed in order to get the most out of the navy aircraft, who still had to fly long distances to reach distant targets. While the smart bombs played a critical role in Afghanistan, it was the Army Special Forces teams down there that were finding the targets, and seeing to it that the air force teams with their special radios were getting the target information up stairs regularly and accurately. The lesson here was that the air force cannot do it themselves.
2- Air and space superiority. The air force has dominated the air over the battlefield for more than sixty years, and doesnt take it for granted. Listing this as a lesson learned is just another way of making sure this continues to be an area that requires constant effort. Against some potential opponents, like China, air supremacy could be lost, at least temporarily. Theres a downside to all this, however, in that the air force spends enormous chunks of its budget on new air superiority aircraft like the F-22. This starves other priorities, and Congress wont give the air force a blank check.
3- Expeditionary operations. In the 1990s, the air force reorganized to better deal with fast breaking overseas situations. New warplane units, designed to quickly move anywhere in the world and quickly set up operations, were assembled. The Afghanistan operation was the first real test of the expeditionary operations concept, and many valuable lessons were learned. It worked, but many problems were encountered that have to be fixed.
4- Precision and Persistence. The air force has been using smart bombs since World War II, but the new JDAM (GPS guided) models proved to be a spectacular success (because they found their target on their own, without a laser or someone to guide them in.) The air force was finally free of the curse, and the cost, of dumb bombs. At the same time, the widespread use of UAVs, which could circle a combat zone for 24 hours or more, and bombers, which, with the aid of air refueling, that could stay up there nearly as long, provided a degree of persistence that had never before been available. All this made air power more effective than ever. In this category, the air force also pays the usual lip service to improving BDA (Bomb Damage Assessment, finding out if you hit what you thought you hit).
5- Airlift and air refueling. These two items are critical mainly because the air force could not get bombs on the target in Afghanistan without the transports and tankers. Less critical, but still essential, in Iraq, both of these non-combat aircraft types are regularly shoved aside when it comes time to get more money. The warplanes take precedence, but there is an ongoing debate over how much air force money should go to the tankers (which are overdue for replacement) and transports (which everyone agrees there are not enough of.)
6- People. Well trained and well led people made it all possible. The air force has continually worked at improving the quality of its personnel. Its easy to take this for granted, but the air force doesnt.
The U.S. Air Force did a study of its first two years performance in the war on terror, and came up with six major lessons learned". These are important things that must be remembered, and that will continue as important aspects of air force operations.