It might be better to try a Vulture first because the FDL takes a more advanced flying technique, which takes a while to get the hang of.
You have to practice one step at a time. Start on small and medium ships. First, try just swapping your pips between shields when the enemy faces you and weapons when you want to fire at it. When you have that automatic, try putting pips to engines when you want to change position. Another thing that helps a lot with small ships is to fly backwards so they can't get you from behind.
When you move onto bigger ships, never let them stay face to face. Boost past them and reposition yourself. They always wriggle around in an attempt to keep pointing at you. Roll 90 deg. And go down their wing. As you roll, they try to copy you, so you have to be quick.
When you feel comfortable with that, Start using your downthruster a lot to rotate around them. That works well on Gunships, Pythons and Anacondas. After that, sidethrusters .
Don't try and do these things all at once in the beginning or you'll get in a mess. Get each step automatic before moving on to the next one.