So here's a simple one, a burst of smoke, very handy when you need a character to zip off screen, or to use in multiples for an explosion of dirt or dust, or even an impact of a character hitting a solid object.
Take that brush tool out and start drawing. The first 3 drawings are the easiest. Shoot them on 1s (meaning have them back to back on your timeline exposed for only one frame each).

Make certain you're working at 24 frames per second too.

Your first drawing should just be a small blob. Draw with the Brush, then fill it in (with a different color if you wish) with the Paint Bucket.
Activate your onion skin move the range finder to only include the previous drawing.

Smoke as simple as this one works well by animating "straight-ahead".

Sometimes I key out some bursts with a key drawings just to see where I'm starting and where I'm going as I build the general shape of the form, otherwisem animating frame by frame usually works. Press F7 to make a new blank keyframe, and with the Onion Skin ON, draw the new expanded shape of the smoke cloud.

Below is the 2nd frame, covering a lot of distance to show the long spacing between the drawings (as shown above). The initial expansion is huge, after these first 3 drawings (on 1s).
Then the 3rd drawing reaches quite large and now from this point forward we can animate on 2s.

Your first 3 drawings overlapping each other should look something like this.
On the 4th drawing the spacing between our drawings (for the outer edge of the cloud's form) is very tight, making the outer rim of the smoke move slowly (all on 2s from now on). Always working with that Onion Skin activated, drawing the outer edge of the smoke cloud is very easy simply trace over top of your previous drawing (on your new blank key frame at frame 4). The spacing between your drawings (for the outer edge) will now always be very small, so as you trace over you're gradually expanding the outer rim of the cloud's shape more and more every frame. The closer you draw over top of the previous drawings position the slower the cloud will expand. Draw with the Brush then fill it in with the Paint Bucket, frame by frame.

Also on Frame 4 you need to start the smoke's break up pattern. Start off with a hole in the middle, this hole will initially start off fast (sort of like how the overall form of your smoke cloud did for the first 3 frames).

So here's a slow motion version of what you should have so far, with some notes along the way:
Here's the Flash CS3 file to download.