I'm sure I'm using the wrong term, I wish I knew the right one so I could search for how to do this rather than make a whole new topic.
I want to create the box that appears in the top right corner of many pages, with notable images and/or facts about the page. Example circled here, in a screenshot I took of The Daily Show's page.
Thanks for your help!
That's called an infobox.
Wikipedia uses complex series of templates to create them. It can be complicated to copy them to your own wiki. See Manual:Importing_Wikipedia_infoboxes_tutorial for instructions.
Sometimes it can be easier to just make your own. Some people use Templates (combined with normal HTML styling) or extensions like Extension:PortableInfobox
