Roughly, here it is:
1) Once you decided that you're going to banana flick a short ball, you step in forward with your right foot forward (for a rightie). The shorter the ball the deeper you need to step in.
2) As you step in, you move your forearm all the way to the back, you also move your wrist back. Ideally, the handle of your racket should point to the opposite wall. You also tilt your racket to the left side slightly so that you brush other the side. Here is how the proper starting position looks like:
https://www.flickr.com/photos/henrylee888/24135833284/in/album-72157661875590584/
3) At the top of the bounce, you brush the ball with full commitment as fast as you can. Don't try to brush it slowly, try to move your racket fast even if you make mistakes at first.
If it is sidespin, no-spin, topspin, or slight backspin, you brush over the side and top of the ball with slight adjustment and finishing forward. This will generate a lot of pace. Against heavy backspin you have two options:
1) Brush over the side-top as it is like no-spin, but finish a little bit higher. This will generate a bullet-like shot, but it requires tremendous racket speed. It is a risky option.
2) Brush over the side of the ball but go all the way upwards. You will generate a slow, spinny ball that can be surprisingly effective as it throws off the timing of your opponent.
The best way to practice it is to ask your friend to feed you a lot of no-spin or light backspin short balls because those are easiest ones to spin. Practicing with a robot can also be good, but only after you have an idea how to do it, because robots usually generate ridiculous amount of backspin that can be tough to overcome.
I personally enjoy this tutorials by Ovtcharov, he discusses many of the questions you ask (e.g. racket head speed in Part 2 at 4:00):
I can post my own video of this shot if you want to see how an amateur player does it.