So I spent the first 10 days looking for and looking at apartments. I saw a lot and sometimes it was enough to have a look at the surroundings to turn back. But some were quite nice and we finally got the one we were dreaming of.
I've outlined the process in Hungarian here -- so speakers of the language head there.
Let me explain how it all works in Geneva. Switzerland being Switzerland other cantons might handle things a bit differently but the general idea is... well... general =)
The land available in canton (and city) Geneva is pretty restricted and you cannot just build away as long as you have the money. So the number of apartments is practically fixed. No need to worry though, you'll get one if you try hard enough. ;)
So the thing is you don't choose an apartment as much as you're chosen. This means that if you like one you have to apply for it, submit your papers (I'll explain) and wait for the person(s) responsible to choose.
In reality it's not that horrible at all. As far as I know it goes like this in many countries so others won't even be as shocked as I was when I first heard it.
OK, so here's what you have to do:
1) Look around. <<- In the sidebar I've listed a couple of sites where you can sort and list and browse at your leisure. Some work in English as well and there are of course others as well. I tried to act as fast as I could because some apartments get rented quite soon (given the situation).
2) Call them and fix a date (La Visite). Sometimes there's a fixed rendez-vous or a number given especially for "visites". Sometimes English works as well but it helps a lot if you speak one of the "native" languages. (It's not a cliché. Here in Switzerland if you want to ask a favor it's best to do in the native language. However, as I'll relate later in the "IKEA chapter" =D English carries authority in some cases.) Most (99%) of the time you'll not be dealing with the owner of the flat. Apartments are owned in blocks (so I've heard) and the task is given to the régie, the real estate agency. (So when they say they cannot recommend you to the owner they're not actually lying but it's worth excercising your magical powers on them :D)
3) La Visite. Just have a good look at the apartment and the surroundings. I always used googlemaps to get there and sometimes the street view was enough to make me cross out the apartment. :)
4) Apply. Most of the time the régie/concierge/the person who arranges the visite will give you a form of application you have to fill in. This has to be handed in along with the documents required: most of the time a copy of your ID/passport; the details of your residence and work permit; the bank guarantee of the deposit (not always needed at this point but carries weight if you have a nice one), etc. They'll let you know which ones they need exactly.
5) Waiting, hoping, wishing. Of course you can "chase" the regie a bit. Sending in chocolates might be a bit too much though :D
If you have stuff to arrange (as we did) you can still get the keys for an afternoon or a day.
Well, we applied for 4 apartments and got 3 (we were a bit late with the third). Among them the one we really wanted. Some regies might charge you if you don't take the offer -- but mostly they don't bother. :)
So, as you can see, it's not so horrible at all!
One has to work hard if one wants to live in Switzerland but it's not hopeless and totally worth it.
Good luck! Hope this helped.