Find a empty server and fly around.
Next learn how to brake and turn it the best way of turning fast. Also don't abuse the afterburners it makes you easy to follow short bursts.
Next learn the maps bits to avoid like the canes on firestorm.
Search for a jet guide from the user Hitman once you got the basics down
I had the exact same troubles when I first played BF3, game after game, I will go up in the sky and only be up for less than thirty seconds, then back on the ground again but now I am a bit above average at flying the jet. My advice would just to watch some tips on youtube regarding jet flying strategies/skills/howto and just keep on practicing which will more than likely improve your flying!