I haven't succeeded in figuring the darn thing out just by popping the hood and poking around. My most urgent task is to understand how to edit HTML on a site that runs entirely on Miva Merchant 4. And I do mean the whole site, not just the online store.
Suggestions?

Most Miva Merchant sites are 100% in Miva Merchant, not just the store, so edits to the global header, footer and category tree are site-wide, saving a ton of work. It's true, though, that it can be tricky figuring it out. Once you "get" Miva Merchant, though, you'll find it a fantastic tool.
There are a lot of free Miva Merchant version 5 tutorials here:
http://www.mivamerchant.com/services/serviceclub/video_basic.html
Most of the basic ideas are the same as MM4. I also have a couple of cheat sheets at:
http://www.merchanttutorials.com/WNH-MM55CheatSheet-Side1.pdf
http://www.merchanttutorials.com/WNH-MM55CheatSheet-Side2.pdf
Right now I only have 4 MM4 tutorials up in the Advanced Tutorials area. I'm working on more. This one might help you the most:
http://www.merchanttutorials.com/Public/MM4wOUIAdminQuickTour/MM4wOUIAdminQuickTour.html
For more info about my tutorials, go to http://www.merchanttutorials.com.
I hope that helps.
Chuck