Make a GIF or a still

Choose File › Export GIF…, or pick GIF as the Format in the Export window. Keep it short and use 480p or 720p to keep the file small. For a picture, press ⇧⌘S to save the frame under the playhead as a PNG.

Export a GIF

Choose File › Export GIF…, or press ⌘E and choose GIF under Format.
Pick a Resolution: 480p, 720p or 1080p.
Pick a Frame rate. 15 or 20 fps look smooth and stay small.
Leave Loop on so it plays over and over.
Click Export.

Keep it small

GIFs get big quickly. To keep them easy to share:

Export just the important part. Press I and O on the timeline to mark it, then choose it under Range.
Under More options, leave Optimize on and raise Lossy. Both shrink the file a lot with no visible change.
Use a lower resolution. 480p is plenty for a README.

Tip

For a seamless loop, turn on Loop in the Pointer tab, under More settings › Hide. The cursor glides back to where it started before the end.

Save a single frame

Move the playhead to the moment you want and press ⇧⌘S, or choose Export current frame as PNG from the Commands list (⌘K). The picture has your background, frame and zoom, just like the video at that moment.

Good to know

The launch pack makes a README GIF and a thumbnail for you, picking the best moments by itself.