Did you know your Mac comes with free screen recording software? It’s located in your Quicktime program. You can access it by selecting Applications from the Go Menu.

Scroll down until you see Quicktime Player, then double-click on it.

The following post by Dave Mark, who was kind enough to allow me to show screenshots from his site, explains the next steps. Please note that the option to record only a portion of the screen requires Mac OS 10.7 or later.
Tips For Making Better Screenshot Videos
Clean up Your Screen:
Quicktime on Mac’s with version 10.6.8 and earlier do not have the option to film portions of the screen – the screen capture will film your ENTIRE desktop, so it’s a good idea to clean up your background by moving files into folders so that it looks nice for your viewer.
To shoot only a portion of the screen, on Mac’s running 10.7, check out this video:
Zoom In:
If recording from the web, I recommend you ENLARGE your browser images so that it is easier for your viewers to see. In Firefox, click on View/Zoom/Zoom In. In Chrome, click View/Zoom In. This makes it easier for viewers to see what you are clicking on.