Full theory from various coaches can be found:
https://trello.com/b/WrQmvekp/table-tennis-tips-compiled-by-dr-mithilesh-dronavalli
Notes are for left-handed pen grip players, but can be generalised.
Chop
Short chops: move the hand beyond the chop, full flexion, or extension. Move the ball around and keep it short. Don’t go too long, as they will loop it. Wait for the ball to drop
The Double Bounce Chop shot. Keep your body in flow with your hand, cut the falling ball under the ball, and use the bottom half of the bat (bottom middle). Return will bounce twice
Backhand Flick
Must judge whether the spin is topspin OR no spin (approximately) or underspin.
Backhand Flick against underspin or no spin or sidespin (without top): Straight lower arm perpendicular (approximately) to the table, brush with wrist around the side of the ball, more flick, less power. Do this while the ball is dropping. For more underspin, flick your wrist like a mini-pendulum around the side of the ball. For sidespin, consider the direction of your flick.
Backhand Flick against topspin: Forearm is parallel to the table and flick on top of the ball and flick forward, not up.
Backhand loop:
Open the angle of the bat (but still slightly closed) around 10-15 degrees forward. For a pen grip, place your thumb on the bat and tilt your wrist.
Place your hand down in the middle of your legs.
Crouch.
Let the forearm dangle loosely from the upper arm by raising the upper arm to the shoulder level. (Wang Hao)
Clock wrist and elbow backwards like winding a spring.
Judge the amount of underspin on the ball by reading the spin on the ball.
Weight transfer from right leg to left leg (left-hander). Move Right Kneecap (Patella) by pointing inwards and Move Left Kneecap (Patella) by pointing outwards using the quadriceps.
Unwind the elbow and wrist (by starting movement with the fingers) and brush the ball around the side of the ball, in an upward direction, depending on the spin of the ball.
If it is heavy underspin, be careful of the timing ( wait a little bit longer) and brush the ball on the fall (“catch the ball”) and send it back.
Forehand loop:
Open the angle of the bat (but still slightly closed) around 10-15 degrees forward.
Crouch.
Judge the amount of underspin on the ball by reading the spin on the ball.
Extend the arm at the elbow, down to the lower leg.
As the ball is approaching, lift your arm (flex at the elbow) in an upward motion. Finish motion with an upward movement of the wrist (by moving the fingers up) for further spin/acceleration. Don’t forget to perform the weight transfer for the forehand (see below) while engaging the core.
Weight transfer from left leg to right leg (left-hander). Move Left Kneecap (Patella) by pointing inwards and Move Right Kneecap (Patella) by pointing outwards using the quadriceps.
Drive against no spin or topspin:
For the forehand loop, keep your arm above the table and move forward with your forearm. Close the angle of the bat by tilting the wrist and pressing with the thumb. Close the angle more for topspin. Do the same for backhand.