One of the questions I'm often asked about Chromebooks is about creating screencast videos. The following three options allow you to create screencast videos on a Chromebook.
With ScreenCastify installed in Chrome you can record everything happening in a tab in your browser. Voiceovers are supported and a pointer is included by default. Completed recordings can be saved to your computer or uploaded directly to YouTube. There are a few things to note about ScreenCastify before you get too excited about it. First, your Chromebook and or Chrome browser must be up to date (that shouldn't be a problem in most cases) as Chrome version 32 or higher is required. Second, while recording the desktop is an option it is an experimental option and may not work as you hope it will. Third, your microphone is turned off by default so you will have grant ScreenCastify access to your computer in order to record a voiceover.
TechSmith recently launched a new beta version of Snagit for Chrome that supports creating screencasts that you can save into your Google Drive account. To use the new screencasting option in Snagit for Chrome you will have enable the "beta" version of both the Snagit for Chrome extension and Chrome app. The Snagit Chrome extension is what allows you to capture your screen. The Snagit Chrome app allows you to save your screen captures in your Google Drive account. You do have to install both the extension and the app for Snagit to work correctly. The video below provides directions on how to enable the beta mode of Snagit for Chrome. The video also shows you how the screencasting works.
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.