Hi christine,
I tried.... but sometimes people tend to break their promises if negociated directly. I wanted a room in June (in UB center town) and we agreed on 150$ a month.... right 1 minute after my train arrived in UB I've got a call that that a**hole increased to 250$. I really hate that and went into a guesthouse's dorm.
You can get some people to share accomodation when contacting local expat organisations like Deutsch-mongolische Brücke (for sure such thing exist for english-speakers as well). Or ask a guesthouse if they can help you, ask your organisation, that sends you here.
The classifieds you can forget - I've seen some offers for 700$, 900$ for a 2-room appartment is far too expensive and some of them want 1 year of rent in advance.
I know some people here who can help to find a room - but that could take a month or two, if you're lucky only 10 days. Best way: go to a guesthouse and tell them what you want.
Houses literally don't exist - man on the street lives in 1-2 room flats in 3-10 store buildings - or in felt tents at the outskirts of the city, and the few villa-alike building owners definitively won't share anything. There'S a villa quarter near the Tuul river.
If you're lucky you find someone who allows you to sleep in the living room in exchange for english lessons, but keep in mind that that often means during the weekend half a dozen people come, and party.