I can give some advice here, but keep in mind I've had about a 100 hours or so flying in HnG, and so I probably have my own style which might not match what other pilots use. I'm no ace in the sky though, let me tell you that.
Personally, in dogfights, I'll primarily use a combination of mouse and keys, but only using the ctrl key on occasion, all the while using 1st person view (use your mouse wheel to flick between 1st person and 3rd person). I'll be using the mouse primarily to "point" my plane at targets, and changing the throttle as need be with W and S keys. When I need to make small turns, I generally do the following:
If I need to make more precise turns, I'll also incorporate the WASD keys. W and S for the throttle, because turning at top speed will mean your turn will be much larger. And S and D for the "yaw", which moves the plane on its vertical axis, and it seems to help me with a bit of extra turning power. This takes a bit of practice to find what works. If you're going too slow you won't be able to execute a very nice turn; if you're going too fast, the turn will take a long time and cover a lot of distance, and make yourself an easier target for other planes and ground anti-aircraft.
The ctrl keys allow me to make turns without worrying about the throttle. Forewarning - as I said earlier, full throttle turns won't be as sharp and as such will take longer to execute and make you an easier target - so, while you're getting used to flying, avoid using the ctrl keys to turn if you have someone on your tail. Experiment with ctrl keys during dogfights after getting used to mouse and keys for a while.
To execute a turn with ctrl keys: 1. hold ctrl 2. press A or D, which will rotate will your plane left or right 3. then press S, which will then move the plane in the direction you want. There is far less precision in turning with ctrl keys. I typically only use them in combination with the "free look" key, which is by default assigned to the shift key.
After a bombing run, or just searching for my next ground/air target, I will use a combination of "free look" and ctrl keys to find my next target. As my "free look" key is assigned to shift, here is where my fingers are and the steps I follow: 1. Finish bombing target/spawning/picking my nose 2. Immediately press shift key with my ring finger, and then use the mouse to move the camera to look for another target 3. Hold down ctrl key with my pinky, and then use WASD with my middle and index fingers to turn where I want to, all the while still holding down the shift and ctrl keys. 4. Find my next target, release shift and ctrl keys, and then return to mouse and normal keys to move towards and target my next enemy.
It really isn't easy being a pilot. Please spend a few ranks in STAGED getting used to dogfights, bombing ground targets, unlocking your WRENCH, getting comfortable with landing and repairing away from action, and at least APCR ammunition.
Note that all planes in WAR mode cost the Generals quite a lot of credits, and there aren't many available in the assault teams. If you find you're crashing/dying a lot in WAR, everyone will STRONGLY recommend you respawn as soldier, and then go back to STAGED to practice your piloting skills there.