Aviation is the mechanic most neglected when starting out, and the one that multiplies the performance of the other two branches the most when used well. The key is order: almost everything depends on securing air superiority first.
Air Superiority
Before any other air mission is truly effective, you need to control the sky over the area where you're operating. Fighters dedicated to air superiority engage enemy aircraft in that region; without winning that control, the rest of your squadrons (CAS, bombers) take much heavier losses and perform worse.
Close Air Support (CAS)
Once you control the sky, close air support becomes one of the strongest land-combat multipliers in the game: it directly bombs enemy divisions in battle, tilting the balance in your favor. A land offensive well-backed by CAS often breaks lines that would otherwise hold.
Strategic Bombing
Heavy bombers attack infrastructure, factories and enemy cities deep behind the front. It's a long-term investment: it doesn't win battles by itself, but it erodes the enemy's industrial capacity over time, especially in long wars against a power with heavy industry.
Common Mistakes
The most common mistake is building every type of aviation at once with no clear priority. It's better to first secure a solid number of air-superiority fighters over your main front, and add CAS and strategic bombing afterward, once the sky is already yours.