apartment

So the choice is made, Berlin. I want to stay there for a while, so hotels are out of the question. They are expensive and you always have to go out to eat. Besides, they aren't fun with their hotel smell and hotel corridors and hotel warmth and hotel art on the walls. Couchsurfing? Great for short trips, but I didn't want to have to find a new place every couple of days, even though it might be easy doing so as Berlin has an active CS community.
An apartment then. Google to the rescue and this site (city-wohnen) came out as one of the most interesting. It's english, offers a good search engine, all the legal stuff is there and translated well and it offered a lot of apartments in the sub-500 euro price range and also for rental periods for as short as 1 month.
Finding an apartment for that price in the very centre of Berlin won't work, but the great thing about Berlin is that it has a huge area around the central part which is still very good connected with bus and S-bahn lines (more about the public transport later).
On this drawing you find the districts of Berlin (small description of the districts here), of which Mitte and Tiergarten contain most of the historical landmarks. Every location on that map however, is spaced maximum 30 minutes of comfortable public transport away from the centre. My apartment is located in the north of Treptow, close to Treptower park and on a 5 minute walk from an s-bahn station.
The price is 490 euro per month warm (which includes heating) and it has all you might want: washing machine, television, flatrate broadband internet, seperate sleeping room, living and kitchen, towels, bed linen etc.. It's not an apartment which is used solely to rent out but an actual house of a German woman now away till the end of the year. I love the place, it's very nicely decorated, very sunny, well renovated, well isolated etc etc.
On the website this apartment came out as one of the best: large, decent location in a district full of young and chill people.
The surroundings are nice, its tidy, very spacious with loads and loads of trees, wide lanes and sidewalks, calm... My apartment is at the back of a block of 5-6 story buildings like there are a lot of here. The only problem are the stairs (no elevator)

After I contacted city-wohnen for the apartment I wanted to rent (add it to your wish-list, register and add your wish-list to your registration) I received a digital contract a couple of days later, with the information about the landlady (in this case the mother of the owner of the apartment), address etc on it. The deposit was, as often, the price of one month and is to be paid together with the money for the first month to the landlord.
This city-wohnen service comes at a price though, a rather hefty one: 25% of on months rent + taxes on that amount. All in all, I pay nearly 30% of the montal rent to the company of city-wohnen (if you rent longer, the percentage of the montal rent is lower, off course).
However, for this I get city-wohnen as a perfectly english-speaking mediator which takes care of all the legal stuff.
If you want a cheaper place, I'd advice checking out the german-language websites offering rooms for rent (often targeted at students, you get a room in an appartment which you share with other people), that should get you a room for as little as 250 euro or less. Example.
Google also turns up some hits which offer apartments at a price per night, stay away from those as they are horribly expensive. Mostly aimed at hotshot professionals staying for a short while, I guess.