I’ve reviewed a lot of screencasting tools over the years (a list of seventeen can be found here). The problem with most screencasting tools is that they require Java. Java doesn’t run on Chromebooks. So if you’re a Chromebook user and you want to record a screencast the way to do it is to use Google+ Hangouts. A Google+ Hangout On Air allows you to broadcast your screen (you can do this even if no one else is in your Hangout). The broadcast is automatically recorded and saved to your YouTube account. Brian Bennett posted detailed directions on the process here. There is a video demonstration at the end of Brian’s post.
Mark Jenkins also produced a short video on the process. That video is embedded below.