Ok... let me do my best to explain how most of the RF cameras focus...
First take a look at this camera body...
The window at the extreme right(facing you) is call the viewfinder window. It allows you to see through the eye piece at the back of the camera.
The one beside it is the frameline illuminating patch. It lets light in so that the framelines are illuminated in the viewfinder. If you cover this patch, the framelines will disappear.
The small little window next to the frameline illuminating window is the focusing patch. If you look through the viewfinder, it's the centre rectangular patch that appears a little different from the rest of the viewfinder. On some older rangefinder, it could be yellowish in colour. As what ziploc has explained, it works by some trigonometry to get an image on focus.
When you take out the lens, there is a round little thing on the lens mount and if you move that round little thing, it actually move a mechanism in the "viewfinder assembly". When mounted with a lens on the camera body, once you get the "double image" in the viewfinder focusing patch overlaps, the image should be in focus.
It's very hard to explain everything in words & diagram... it's like explaining how Mona Lisa smiles... it's best to hold a rangefinder camera in your hands look through the viewfinder and focus. Any fifth grader should understand how it work after fiddling it for a while.
Basically, a rangefinder camera main difference from SLR or DSLR is: it does not have a mirror box in the camera body. Hence, you do not focus through the lens. Hence this (T)hrough (T)he (L)ens word is loosely connected/used. I would rather say it is NOT (W)hat (Y)ou (S)ee (I)ts (W)hat (Y)ou (G)et [WYSIWYG].
Having said that, RF cameras, is not ideal for macro & close-up shots, as minimum focusing distance is 0.7m & it's not WYSIWYG & it introduces something call parallax error for close focusing. But it is great for street and documentary type of photography. Why? Because it is small in size, subjects simply do not feel that they are pointed by a big gun! And you can open both eyes to shoot and anticipate activities OUTSIDE the frame. (Not that you can't do it with SLR, but it's easier with the RF camera).
Having used SLR and RF, personally, I feel that SLR make you place emphasis on getting the subject in focus, while RF allows you not only get the subject in focus, but also frame the picture better (using the framelines for composition). [Hard to explain how & why... just a personal feeling]
Hard to explain all the advantages, it's like describing why an apple a day keeps the doctor away... You just have to grab hold of one and start using... you might like it or hate it. It all depends on your shooting style. If you are a machine gun shooter, take no prisoners, then RF is definitely not for you.
If you are a one shot one kill... take time to compose, understand your subjects, appreciate the beautiful surroundings, talk to your subjects appreciate fine mechanical machines, then, maybe RF photography might suit you better...