On OSX you can capture videos with QuickTime Player (which comes with the OS).
- Start QuickTime Player
- Hit ^⌘N to bring up the window for screen recording
- Hit the record button
- Drag the mouse to select an area you want to record, or click to record the whole screen
- When you are done recording just hit the stop button in the menu bar
- QuickTime Player will create a new video which can be saved
Once you are done you can simply use one of the many online services (e.g.: this or this ... there are lots of them) to convert the video to a gif.
Example output:
