This might be a stupid question (I'm new to typesetter), but how can I add buttons to a page?

That depends upon which kind of button, and whether You have a button-plugin installed  from webinstall or in ckeditor

1. Bootstrap button

2. Css - Button ... (some examples)

Generally You must go into the sourcecode and add one of the above example - codes into the source - at the place where You want to place the button.

* You can also add a bootstrap 3 button (or github )  to ckeditor (from the harddisk)

You can also try this Simple_Button plugin

The simple-button plugin has the disadvantage that it is only accessible from sections-menu  - and it has only 4 horizontal and 4 vertical positions.  Its code is like

<div class="sb-wrapper sb-middle sb-left"><a target="_self" class="btn sb-gray sb-default sb-solid sb-3d sb-emboss" href="#"><span class="sb-buttontext">simple</span></a></div>

What ckeditor would need is a css-button - plugin. ( or html-button) so that the button can be anywhere in the text.