There are many ways to record a video with a Mac, but we're going to focus on a way that will work for most Mac owners. This assumes that you have a Mac with a webcam. The webcam may be built-in or an external device.
We will show you how to record a video easily using Photo Booth, an application that is bundled with macOS. You'll find it in the Applications folder. Open it, and select the video option from the row of icons in the bottom-left corner of the window. It's the third icon.
If you have more than one camera, you can select the camera you want to use from the Camera menu.
If you are reading your auditon piece from a script on screen, you may want to position it near the camera, so you appear to be facing the viewer.
When you are ready to record, press the record button in the center of the bar at the bottom of the window.
When you are done, click the same button again (it now looks like a stop button, with a red square in it) to end the recording. Your video will be added to the right-hand end of the row of thumbnails at the bottom of the window. From there you can drag it to a Finder window or the desktop to export the video file from Photo Booth. Or you can select it and use the File->Export… command. Save it to a known location so you can continue to steps needed to post the video on the internet and get a link to it.
To find out how to post the video and copy a link to it, check out one of these topics:
Posting an Audition Video on Google Drive