Best done in Versus Mode, 1vs1 match. Two controllers required.
After selecting your character(player 1) and a dummy character(player 2), you'll be given 5 selectable levels for each player.
For Player 1, select Level 5 P HD Max. This will start with a full HyderDrive gauge, which you can see above the Super Meter on the bottom of the screen.
For Player 2, select Level 1 HP 50%.
HD cancels are performed by canceling one Special Move into another Special Move while in Hyper Drive Mode.
For example purposes, I'll use Terry Bogard. Get within a few steps of your opponent and activate HyperDrive mode by pressing LK and HP at the same time. You'll see an aura around your character when it's activated, and the HD gauge will rapidly deplete.
Once HD mode is active, use Terry's Burning Knuckle, once it connects, quickly enter the command for Terry's Crack Shoot.
Notations are as follows:
Activate HyperDrive Mode by pressing LK and HP simultaneously.
LP Burning Knuckle: D,DB,B+LP.
As soon as the move connects, or while it's still active, input:
LK Crack Shoot: D,DB,B+LK
If done correctly, the Burning Knuckle will HD cancel into the Crack Shoot, and you'll see "HD Cancel" pop up below your health bar. It doesn't matter if the second special move connects, you only need to cancel the first special move into the second for the HD cancel to count.
You should be able to execute 3-4 HD cancels before the HyperDrive meter runs out, then simply KO your opponent in Round 1 and 2 and hit restart and do it again. Should take about 15-20 matches.
If you're using a different character, keep in mind that Projectile/fireball attacks cannot be canceled into another special move.
Selecting 1vs1 with Level alterations is the fastest way I found, as doing 3vs3 you'll have to do a lot meter building. Use your Max gauges in Round 1, then KO your opponent's half health in round 2.
If you've played Street Fighter, both of Terry's moves are reverse fireball motions.