Playing as a soldier, air-strafing to the left is easy – all you need to do is shoot to the right, jump and hold the crouch button while turning left.
On the other hand, strafing to the right seems to mess up all the time. I suspect that this could be because the soldier's rocket launcher is on his right shoulder so shooting to the left in order to begin air strafing to the right is awkward.
Best Answer
The easiest way to accomplish this would be to follow these steps:
The trick with this one that requires practice is facing forward after shooting a rocket behind you. It's a fine art, but then again the entire practice of rocket jumping requires finesse.