The preferred method, in my opinion, for putting a gun back into the holster is:
Bring the gun BEHIND the holster, then push the muzzle into the holster "under" the strap. this will use the top of the slide to push the strap out of the way, not the muzzle or trigger guard. With most guns, you can also place the index finger along the side of the trigger guard, forming a wall to keep the strap from entering the trigger area.
you do NOT want to cross the weak hand over for two reasons:
1. You will likley "paint" yourself (ie- cover your own hand with your muzzle).
2. you may not have to hands to reholster with on the street.