There are a lot of tools out there that are capable of offering screencasting. Some of my favorite include Screencastify or utilizing a Quicktime/iMovie combo. However, Apple IOS 11 now brings screencasting to your iPhone or iPad.
To do this simply access the control center on your device –> click on “customize controls” –> and then click the “plus” sign next to “screen recording.” A control panel will pop-up with a variety of “player” options, similar to that of a dvd player. Click on the “record button” located in the lower left of the control panel.
Note: a button or two above the record button is the “screen mirroring” option. This is what you would access if you want to cast your device to an apple tv.
What even cooler? You can also record audio, so you can add voice over/discussion to your screen recording. When you are done, simply click the “record button” again to turn it off. Send this to yourself as a file, and if you want to edit/tweak it, you can also bring it into iMovie to do some editing.
Hope this helps!