Try hold the right trigger, get your speed up than start holding down on the right stick. keep flying high and straight and start messing with the sticks and you should pick it up pretty fast.
Another tips you have to try is banking turn, to do this let the jet turns brief (increase the throttle, roll and climb) and make sure to have enough altitude to soak up the height you lose while turning or you will crash.
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Move on to next tips about attacking ground targets, Sure you have to nose down the Jet or aircraft but is so risk of crashing, that's why preparing for a strafing run is more important than hitting your targets because once you have properly prepared your run, the attack should be easy. Preparing is by gaining altitude. The longer you intend to blaze gun and engage your target, the more height you will need.
Dont forget about the range or stretch of area that you are willing to attack. If your target is a single bunker or hardpoint, you may only need a single pass to deliver an AGM88 HARM. On the otherhand, if you need to blaze away and destroy a group of vehicles on the opposing team, you may want to give yourself more height/time to make your attack.
beside how to fly jet in battlefield 3 you can also read jet control diagram for Xbox 360, PC, and playstation3 on this site.
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