Turn on Show a teleprompter in the recording options to put a script on screen while you record. Choose one of your Documents as the script, or type one in. The teleprompter shows the Document's current content rather than a copy, so editing the Document changes what you read.
It sits at the top of the screen, above the recorder, so your eyes stay near the camera. Set the text size and width in the options and drag the handle on its bottom edge to change its height. Scroll starts and stops the text, the space bar does the same, and the speed slider sets how fast it moves. Turn on Mirror the text if you are reading off a teleprompter glass in front of the lens.
The teleprompter is part of the page rather than part of the video, so it is not recorded - unless you share your entire screen, in which case everything on that screen is captured. Share a window or a tab to keep it out.