What I was getting at is what part of your opponent's body are you targeting. It sounds like you are thinking in the ring and that is really where it all starts; you have to do your roadwork and your sit-ups, but the most important part of your body, in boxing, is your brain. (maybe I'll trademark that?).
To slip left- do you mean to your left?- and counter with a hook is very short and sharp move. Weight goes to the left foot, turn your shoulders to your left, then hook coming back. Very short and sharp. To slip to your right and counter with your right, drop your weight onto your right foot and, as you transfer it back to your left foot- as you throw your right hand- pivot a bit to your right. You are basically following his jab home.