I'd suggest reading
Phil Askey's review of the M8 when it came out. It's a great description of what a rangefinder is and does from a dSLR POV. Askey had never shot with a RF before the M8, and was so impressed with it that he ended up buying one. His review of the M9 is also quite good.
The big difference in operation is how the scene is displayed. With an SLR, the light coming through the lens is reflected by a mirror box up into the viewfinder. With a rangefinder camera, your viewfinder is separate from the lens, and you're using a rangefinder to focus, essentially you're focusing by subject distance. If the camera has a coupled rangefinder, you get the superimposed bit between the viewfinder and the rangefinder, and you're focused when the two images coalesce (RF cameras tend to be manual focus, btw. No autofocus).
But the BIG thing to remember is that
you're not looking through the lens. Your view doesn't change with your focal length. You see past the edges of the frame at all times, and you have frame line "guides" in the viewfinder. But the upshot is if you're using a telephoto lens, you're trying to compose/focus with only the center portion of the windows. Using telephotos is a PITA. Macro work, too. RF cameras rock, though at the wide angle and normal stuff. And both the camera and lenses are smaller, lighter, and more discreet than an SLR would be.
And without a mirrorbox/EVF/LCD to give you WYSIWYG composing, you get better at previsualization, and simply seeing an image
without having to put the camera to your eye--you train your eye just that extra bit harder. Just as working with film make you learn to self-edit a little harder than digital does, and working without metering teaches you to guesstimate exposure settings by sight. Sometimes not having a tool can help make you a better (or at least more competent) photographer.
SLRs are better for a bunch of other tasks, but where an SLR typically sucks and a RF is king is in street shooting. Street shooters, up until Leica started making digital Ms, really didn't have a good high-quality digital tool of choice. And while back in the day everybody made rangefinder cameras, today, only Leica is left standing. Zeiss makes a film RF, the Ikon, but they haven't created a digital version. Which, unfortunately means no competition, prestige badging, insane collectors, and crazy pricing most people can't afford.
This is also why micro four-thirds is raising such interest. It's another format that, while not an RF, offers a lot of the same advantages that RF cameras did.
BTW, for a good bunch of "relative size" images, check out
The Online Photographer.