CP8: How do I output user input from a textbox to the screen?

Each Text Entry Box has an associated variable, its generic name is the same as the TEB (I prefer to change it to a better name). You can insert that variable in a text container (caption or shape) like any other variable using the X button in the Character part (I cannot post a screenshot, ignore the version you are using, could be anything since 6).

You cannot use a variable as a label on a button. You can insert a variable in the text in a shape, which behaves as a text container. That is another big advantage of a shape button over a normal button: you can make the label dynamic by using a variable as label.