Go into the docking tutorial and keep trying; you'll get it.
Firstly, take it slow. Keep throttle in the blue zone or slower until you get the hang of it. Slow right down before you come to the pad, use your lateral and vertical thrusters to fine tune your approach.
I recommend - if you're using mouse and keyboard, actually changing the default keybindings. The default are kinda wonky and all over the place - I use a setup where mouse left/right is yaw, mouse up/down is pitch, WASD represents forward/left/back/right thrust (this is much more intuitive for people experienced in FPS and other games), roll as Q/E, and R/F as up/down. Mousewheel is my throttle.
Using that set up, as I enter the mail slot I roll Q/E to be in the right orientation facing the pad. When you clear the mail slot, the tracking bead on your compass will actually change to show the position of the pad you're aimed for; it's helpful if you can't see it straight away.
As I approach the pad I mousewheel thrust down to zero, come to a stop, then fine tune my approach using short quick taps on WASD. Once my ship's centered over the pad, F to go down.
For outposts it's a little more complicated, perhaps, but the slow approach and careful lateral thrusting to finish up is still the best way to do things.
I sincerely hope you have 'auto-rotation correction' on in your options menu (right side menu in the ship). If you don't you're just making things difficult!
