The basics of animation
An animation is a row of frames. Each frame holds the sprite in one position, and played one after another they make it move. This smoke has ten frames.
Every frame has a duration. The standard one is 100 milliseconds, a tenth of a second, and that's what we use here, so ten frames make one second of smoke.
And the most useful tool for animation: onion skin. It shows the previous frame faintly under the one you're drawing, so you can see how far things should move. You can show more frames than one, but just the previous frame is usually the most practical. In the trainer it's the red ghost under your drawing.
How smoke moves
At the start the smoke has no real shape. For the first three frames it expands. From frame four it starts falling apart, and with every frame there's less of it, until only a couple of pixels are left. That's the whole cycle.
It uses just two colors: a light grey-blue mid-tone for the body and white for the highlights. The light comes from the top left, so the highlights go on the top, mostly on the left.
How I draw it
Fill the background first, on its own layer. Then when you add new frames, the background is already in every one of them, and you don't have to repaint it ten times.
Draw the smoke on its own layer. On each new frame, delete what's there and draw the new shape, with the onion skin on. Don't be strict about the shape. It's smoke moved by the air, so yours can differ from mine, and that's fine. When a frame gets complicated, draw the outline first, then fill it.
In the video I draw the shapes on all ten frames first, then add the highlights on a separate layer at the end. In the trainer each frame comes with its highlight, so you can check it in one go. Press Play now and then to see how it moves. That's the fun part.