Here's a video clip from Stunt Bike Island. 

New players sometimes have a hard time figuring out how to do stunts.  First of all, you have to hit the S key to do a stunt move.  Second, you have to be in the air to do a stunt.

Here's a step-by-step walkthrough for pulling off a stunt:  First, get going fairly fast.  Next, scan the terrain for a nice surface, ramp, or hill that you could get some air off of.  Hit the incline and then hit the SPACE bar to hop just at the top of the hill.  This should get you high into the air.  As soon as you lift off, hit the S key to perform a stunt (and double the points you'll get for that jump).

To get even more air, and give yourself time to do multiple stunts before landing, max out your hop and speed power-ups (shown in the lower right).  To get more hop power, collect the flower power-ups.  To get more speed power, perform stunts without crashing. 

Enjoy!