How do I create a custom layout template? Is it as simple as grabbing one of the core layout templates and then modifying it? If so, where do I put it? I'm sure this is fairly easy, just haven't done it before.
Yes, you can copy an existing layout from root/core/layouts modify it and put it into your own layouts directory in Backdrop root directory root/layouts/.
For more info, see: https://api.backdropcms.org/layouts
Also, you may be interested in the new flexible layout templates feature that has been added to Backdrop CMS v. 1.14 (less than one week old). This new feature allows you to create custom layout templates in the UI of Backdrop. I hope to create a video this weekend on flexible layout templates and will post a comment here once I do.
EDIT: I have posted a 10 min video tour of new features in Backdrop CMS 1.14. A significant portion of the video is about the new flexible layout templates feature.