Before you start lesson 1, go to the homework and do step 1.
Lesson 1: The right grip. The Continental Grip. If you don't like my picture and video, please search YouTube for 1000 better videos on the Continental Grip. Here are my versions:
Picture: This is what the continental grip looks like. If you are holding your racquet upright, for right-handers, the edge of the grip that points up and to the right (where my finger is) should run into the knuckle of your pointer finger.
Wrist Pronation: One of the things to learn when serving with a continental grip is to turn your wrist out like you are waving to a friend. Your Shake-Hands grip has your pinky down, but when you want to hit the ball, you want the face open to the ball, so you "pronate your wrist" and turn it out. Check out this video:
Get your phone and go outside and take a video of your current serve motion. Before taking the video, take several practice swings and try to remember exactly what your serve actually feels like, not what you want it to look like. You'll want to have this later so you can look back at your improvement.
Grab your racquet with the continental grip.
Do just like the pronation video. Bounce the ball, pronate your wrist to hit it back down with the racquet. Catch it. Repeat 10 times.
If you are pronating correctly, the ball will not be spinning after you hit it.
Now, do that all 10 times. So, that is find the grip, do 10 bounces. Let go, find the grip, do 10 more. Let go, find the grip.... So, 10 sets of 10 bounces with finding the grip 10 times.