The second step of the overhead is to swing to contact and then follow through. Once you’ve completed your preparation by getting your body sideways and getting your arms and racket into the trophy pose position, you need to step forward with your front foot to get your weight moving into the shot.
When you actually swing at the tennis ball, the mechanics are going to be almost identical to a service motion. From your prepared position, the tennis racket drops down behind your back and your non-hitting arm should fall downward to your body. Your racket, hitting arm and non-hitting arm will get to a position that looks almost exactly like the racket drop position on your serve. Next, swing up on edge towards the tennis ball and pronate shortly before you make contact. You want to make contact out in front of your body when your arm is fully extended. You then follow through by continuing to pronate and bringing the racket smoothly around to the other side of your body.
You can see this in action starting at 0:50 in the video above. I’ve completed the preparation for my overhead and you can see that my body is sideways and my upper body looks like it is in the trophy pose for a serve, except my arm is pointed at the oncoming tennis ball. The first thing I do is step forward into the court to get my weight into the shot, and then the tennis racket drops down behind my back like the racket drop position on a serve. Also notice that my non-hitting hand simply drops down to my body. When I swing up at the ball, I swing up on edge but then pronate as I get close to my contact point. I make contact out in front of my body when my racket and arm are fully extended above my head. I finish by following through smoothly to the other side of my body.