A few things used to make this process a little less painful.
First, Safari used to download things to the desktop. This meant the DMG file was sitting right there, looking ugly, taking up space.
Second, Safari used to, by default, open "Safe" attachments (which included disk images), and open the Finder window to the newly mounted image automatically.
The upshot was that, assuming the developer had made an effort to indicate what to drag where with a big honkin' arrow, after your download was done there would be a pretty clear sign of what to drag where to install the app. Unmounting an deleting the DMG has always been an issue (and the internet-enabled DMGs are better for this), although only the unmounting bit is unique to OS X. Under Windows you're still going to have an installer file lying about that has to be deleted.
Both of these things went away, though, and many developers haven't caught up with the times.