Each installed theme can be "inspected." This provides an overview of exactly which page types the theme includes, and the files each maps to in the theme's folder. If you're curious how your theme works, this is a good place to start snooping around.
Install New Page Types
The Inpsect page is also where one can install new page types. If your theme was not set up to install its custom page types automatically, you will need to install them from the theme's Inspect page before using them. Here's a custom theme I'm working on, and I've created a new page type called "Three Column":
Notice that other themes in my site have already registered page types with the other handles: full, left_sidebar, etc. But the three_column handle is new and not already in use. To install it, make sure the checkbox next to "Create page type" is installed and click OK.
Your page type is now ready to use! One thing to keep in mind, though, is that the page we're working with will need to use our custom Fancy Yogurt theme in order to see my new Three Column page type; no other themes currently use a page type with that handle, so they'll use their page type with the "default" handle as a fallback.