Agreed on the tutorial.
Last time I tried it my stick maps didn't work at all, so I didn't even get off the launch pad.
Like Rivet said, the best way to get started is to launch your ship into Drone Sim > Free Flight.
Spend time flying around asteroids using every movement control:
-Vertical Strafe
-Lateral Strafe
-Forward / Reverse Strafe
Practice using thruster options (especially in turns):
-Spacebrake
-Boost
-Afterburner
Cycle through IFCS flight modes on/off and observe how it affects flight:
COMSTAB
GSAFE
COUPLED / DECOUPLED
Also:
LAM (Look-Ahead-Mode - default)
--I recommend disabling to start with.
IM (Mouse interactive mode)
RM (Relative mode)
--This is where I would default. It gives you direct control of your ship.
Learn how to approach / land / takeoff from the landing pads. If you are using M/KB, cycle between SCM (combat mode) and PRE (precision mode).
After you've gotten comfortable with flight, jump into Drone Sim > Vanduul Swarm.
I do hope they continue to work up a good tutorial. There's so much to just ship flight and combat in this game that it really needs one for new players so they don't get overwhelmed. I also think a non-lethal Vanduul Swarm option would help new players a lot with learning targeting systems and aiming options. Those things can be hard to get down when you're staying busy just trying not to get shot.