I picked up the flying controls pretty fast, but that might be because I've always liked flying both planes and helicopters in Battlefield and such. The aircraft are actually very similar to the gunships of BF2142, if you ever played that, with the addition of vertical thrust at all times.
Speaking of that vertical thrust, I think it's the most important part of flying in PS2. When I fly, I have spacebar pressed at almost all times, the only exceptions are when landing or going through tight spaces, really. Using vertical thrust and pointing your nose slightly downwards will increase your cruising speed slightly and using it while banking will reduce your turn radius.
I actually managed to start doing fairly well consistently a few days ago when I realized that the key to actually getting kills is to do everything fast and hard. Tanks? Go low and fast around to their rear and unload as many rockets you need (8 for a prowler/magrider with a reaver) and then boost away and repeat. Infantry is basically the same, approach low and fast from unexpected angle to avoid attention of burster MAXes, unload rockets/nose gun and boost away. Most ground AA looks at the sky towards the enemy, so approaching low from behind usually means that they won't fire at you until you're getting out of there, when it's too late.
Enemy aicraft? Approach from angle, preferably not in their FOV. Never chase for more than roughly 10 seconds or you'll end up too far from friendly lines and get mobbed by enemy fighters. Most AA fighters look for targets along the horizon from high up, so approaching from below and slightly behind is often very effective. The ten-second-rule also means that I never run with AA missiles any more, the lock-on time is simply too long to enforce the rule and in the time it takes to lock you can do more than double the damage with the rotary (AA) nose gun if you're hitting your shots. The key to dogfighting is picking you fights, never head into a fight where the enemy is coming head on (or even sees you, in the optimal case) if you can avoid it, it's simply too risky. Run away from such fights in time instead. Going low and fast helps a lot here, since weaving around obstacles will give him a much harder time to line up shots and you want all the time you can get to get behind friendly lines so that he either bugs out or gets shot down by friendlies.
Finally, the most important thing is situational awareness. Always remember where you are likely to have friendlies and where the very solid rocks, trees and other miscellaneous deathtraps are. It happens too often that I take fire during an attack only to boost off into the nearest cliff face/base structure/large plant and die in shame.