Okay, I know there's a search function, and I know that if I spent the time I could likely find this answer elsewhere in the forum, but only because I was told to ask away, I'm asking the one dumb question I've been able to formulate so far. I promise to search and keep on topic hereafter.
I installed Firefox, which was remarkably simple. When asked if I wanted to install the downloaded file, I answered yes. After the installed did its thing, each time I opened Firefox a disk image icon would appear on the desktop, which I'd need to eject if I didn't want it anymore. I copied the .app to my applications folder and deleted the .dmg, which elminated the icon popping to the desktop, and now it's in the applications folder which is where I'd expect it. The questions in all of this are: how does app installation work in OS X, what are disk image files, and is what I did an appropriate way to manage my applications?