What Roger said! And I'll toss in a few little things.
Sometimes, it helps to think systematically, kind of like a check list.
Top to bottom:
LOOK BACK to be sure there is no one just behind and downwind of you. Keep it safe!
Move your back hand back, or farther out on the boom.
Unhook quietly without letting the board "feel" you do it. Keep your speed up. Most folks, when learning to jibe, either lose speed at this point, or don't have enough to begin with. Scary fast is the ticket.
Hang down on the boom, keep the mast foot pressure on, as you move your back foot across the board to the other side.
There is lots more to the jibe/gybe but all these things help to get you started.