How to make a frame by frame animation for free
Draw frame by frame animation in Paint by Zaweba with animated layers, cels and red and green onion skins, then play and export it from the Timeline.

Frame by frame animation in Paint by Zaweba starts from Layer > Animation, which makes an animated layer where each frame is a cel you draw on. Onion skins show the earlier frames in red and the later ones in green, so you can see the movement as you draw, and the Timeline plays it back. When it's done, export it as a GIF, WebP or PNG sequence, or as video when the suite's FFmpeg is installed.
Hand drawn animation is just a lot of pictures shown quickly. The tools here are there to make drawing those pictures less fiddly: adding cels, holding a drawing for a few frames, and seeing the neighbours through the paper.
Setting up
Create a new document at the size you want the animation to play at. Then choose Layer > Animation and make a new animated layer. Open the Timeline from the View menu. Set the frame rate and playback in Frame Rate and Playback: loop for a repeating cycle, ping-pong to play forwards then backwards, or play once.
Put a background on an ordinary layer underneath. It stays still for every frame, so you only draw the moving parts.
Drawing the frames
On the first frame draw your starting pose. Add a blank cel for the next frame, or duplicate the cel when the next drawing is only a small change, such as a blink. Hold previous cel keeps a drawing on screen for longer without copying it, which is how you slow down a pause.
Turn on onion skins. Earlier frames appear in red and later ones in green, faded so they don't overpower the current drawing. Adjust the falloff to see more or fewer frames either side. Animators usually draw the key poses first, the extremes of a movement, then go back and fill in the in-betweens with the onion skin showing both keys.
Use a light, fast brush for roughs. Once the movement works, add a new animated layer above for clean lines, and another below for colour, so changing one doesn't mean redrawing the others.
Mixing in keyframed movement
Not everything needs to be drawn. A whole character can slide across the screen on a keyframed position while its legs are drawn frame by frame. Keyframes cover position, opacity, scale, rotation and more, with easing curves, so you can draw a walk cycle once and move it along.
If you already have a set of drawings on separate layers, Make Frames from Layers turns them into frames in one go.
Common mistakes
Drawing every frame in full detail before testing the motion wastes hours. Rough it, play it, fix the timing, then clean it up. Another is making each drawing too different from the last, which makes the movement jitter; small steady changes look smoother. And keep frame counts sensible for GIF exports, since every extra frame adds to the file size.
Exporting
Export Animation writes an animated GIF with Paint's own optimiser, animated WebP, a PNG sequence for use elsewhere, and WebM or MP4 when the suite's FFmpeg is installed. Keep the .ptx file as your master so you can edit frames later.
Paint by Zaweba is free and works offline, so you can learn to animate without paying for a separate animation program.