Check to see if you have the Screencastify extension already installed in your Chrome browser. If you don't see that pink arrow icon with the camera in it, then go to the Chrome Web Store to download it for free.
Once you install it, click on the icon in the extension bar.
Then, if prompted, sign in with Google. If you're not prompted to do this, skip this step.
Next, give Screencastify access to your microphone and camera. Be sure to click Allow for every popup that appears. You also may not have to do this part either if you've already done it.
Once you have access, you can click on Browser Tab, Desktop, or Webcam Only to choose the recording settings and see the More Options for each type of recording.
Each option also includes the microphone, and (except for Webcam Only) the ability to embed the webcam while recording your screen. Be sure to test the microphone before recording to make sure it's picking up your voice. A small green indicator will show that your voice is coming in, as noted in the screenshot.
Browser Tab:
This will record only one tab that you choose, and will not change if you switch to another tab. In fact, you'll get a notification that you're recording on a tab in the background if you do switch. The More Options include a countdown, showing drawing tools which allows you to draw while recording, and tab audio which will include audio from any videos or audio playing on that tab alone.
Desktop:
This will record everything on your screen including other tabs, apps that you open, files you open, and anything else that you see while recording. The More Options for this choice include the countdown, the drawing tools, system audio which will pick up anything playing on the device including downloaded audio files, and a webcam preview which will show you what the webcam looks like while you're recording.
Webcam Only:
This option includes only the countdown in the More Options. This mode will record only what is appearing on the camera you choose. It will not capture your screen.
Once you have your settings good to go, record your screen or camera by clicking the blue Record button at the bottom of the pop-up. While recording, if you have "Drawing Tools" chosen, a small grey box with those options will appear in the bottom left corner of the screen. This will allow you to change the type of cursor, choose a color for the pen, pause and stop the recording, or turn on and embed the webcam.
You can stop the recording by clicking the pause button on the grey box, or click on the icon in the extensions.
Once you stop the recording, a new tab will open and your video will appear. Once it appears, it will begin saving to your Google Drive unless you've changed that option. If you changed it, it will save to the hard drive of your device.
Note: You can change these settings by right-clicking (or two-finger clicking on a Chromebook) on the Screencastify icon in the extension list and choosing Options.
Once you've finished recording you now will have the video in a folder in your Drive called "Screencastify". You can also do other things with the video through the menu to the right of the video in your viewer.
Here you can share it from drive by clicking Copy Sharable Link, you can share it to Google Classroom or YouTube, or you can embed it in a website with the embed code.
By clicking on Download, more options appear including downloading as an MP4, exporting the audio as an MP3, or downloading it as an animated GIF.