One of my favorite websites for creating screencasts is Screencast-O-Matic.com. The basic service is free. You can record up to 15 minutes of video for each video you create and can download the video directly to your computer or post to YouTube without even creating an account. If you create a free account, you can store your videos on Screencast-O-Matic and use a link to share your creation.
With the paid version of the program - which is ONLY $15.00 a year by the way - you can create longer videos and it provides you with a great little toolbox of editing tools like overlays, cutting tools, audio inserts, and more. I gladly pay the $15.00 - it is my go to tool for screencasts and I think it would be an outstanding tool for teachers that are flipping their classroom or just want to post tutorials for their students. Here's a short video I found on YouTube that shows how to use the site - https://youtu.be/xiTymQcKGeE.