Q:

How do I perform a high speed car jack? 

There is a control called "Active Hijack" which I have got bound to Q. This button makes me open my car door while I'm driving and as I pass cars an arrow highlights indicating I can jump onto that car, presumably to hijack it. 

However, when I press the jump key, I faceplant into the back of the car and lose a lot of health.  
How do I perform a high speed car jack? 

A:

The 'Action Hijack' key (Default Q) is the correct key, but there's a trick to it.  Hit and hold Q to pull up the interface where Wei is hanging out of the car and the white arrow appears, then hit Q again when the arrow turns green.  I hope this helps clarify the confusion for anyone in the future. 

A:

It sounds like you're hitting the jump button instead of the "Action Hijack" one to perform that final jump. 
From the official manual or steam manual:

While driving and approaching another car, you can use left SHIFT to
  leap between the moving vehicles and perform an ACTION HIJACK.  When
  the white arrow pointing towards the target vehicle turns green, tap
  the left SHIFT button to leap and take control of the other car. 

Both manuals state that left SHIFT is the "Action Hijack" button but the in game default seems to be Q so just replace left SHIFT in the above with Q or, if manually remapped, whatever you have it mapped to.