Use a sheet with a hole inside.
Then in After Effects replace the hole by the black spot.
To insert the black spot on the sheet, you can use the technique that I use here to add the red X:
Finally, you need some masks on the arm to add parts of it in front of the black hole.
You can do this with the technique I show in part 4 of this tutorial to place the fingers in front of the screen insert:
You need to know about tracking, masking, and layers. You must treat each shot in your sample video as a separate project. Here's one approach.
- Create your sheet with the black spot as a prop
- Create a duplicate prop with a hole in the sheet
- Carefully film the scene with the camera locked down
- First take move the prop with the black spot into position
- Second take replace the prop with the spot with the prop with the hole and move your hand through the sheet
- Last take move everything out of the shot and shoot a clean plate
Inside AE load up the first take, second take and clean plate in a timeline with the clean plate on the bottom and the first take on the top
- Trim the first take so the out point is where the sheet stops moving
- Trim the second take so the in point is where the sheet stops moving and you are getting ready to put your hand through the sheet
- If necessary roto the first take to remove your body to line up the shots
- Use mask tracking to track the hole in the sheet
- Copy the mask to a black solid the same color, and if you want to get real fancy the same texture as the prop with the black spot
- Add an additional mask to the solid to cut off the hand as it goes through the sheet
- Layer appropriately
What I'm trying to say is that the AE part is fairly straight forward if you have properly set up your shot when you filmed it. As you get better at planning you'll be able to use a moving camera.