This will both speed up your play, and, I really believe this, it will improve your play. You watch the pros, everyone of them does the exact same thing over every shot, including their putts. I walk to the side and take a full swing. Then I set my feet and hands, look at the target, then I pull the trigger. Without a pre-shot routine, you can become indecisive.
Indecision causes nerve problems.
You freeze over the ball and you wind up hitting a bad shot. As anybody knows, bad shots translate into slow play. There's another factor that comes into play, especially at the club level. Carts can really slow a round of golf if the players aren't thinking. Players don't notice yardage markers, and usually they are painted right on the paths.