Outside of towns and cities camping is very easy in Mongolia, just find some where you fancy and park. The only thing to be aware of is that in the country side Mongolians are curious, they like beer and food, see no reason why they should not simply take your beer and food without asking, and can turn into guests that apparently have no desire to leave and let you have your camp to yourself. Be prepared to move on as a last resort.
In Ulaanbataar we parked at the Oasis Guest House on the eastern side of the city. It was a very welcoming place but also very tight for a vehicle the size of ours.
In smaller towns like Moron and Olgi we found a yurt stay with a big yard and parked there.
At the western border we spent a night in the town right at the border gate and parked in a hotel compound.
The following links will provide downloads of our camping log for Mongolia in either GPX or plain text format.
We were told that Mongolia gets most of its fuel from Russia. The price seemed to confirm this as it seemed a bit more expensive. Typically diesel fuel was between 1800T and 2000T per liter. At the time of our travels in Mongolia the currency was 1400T to the US dollar which translated into a fuel price in the range of $4.80 $5.30 per US gallon.
Like in Russia we occasionally saw fuel stations advertising Euro diesel. But this was only in Large cities in the country side there was only "plain" diesel.
Fuel stations generally had a person dispensing the fuel so that one could indicate "fill it up" with hand gestures.
On our northern route across the country we found fuel stations abut every 100-150 km even in some very small towns. Fuel was easier to get than cheese and vegetables.
Be warned Ulanbaatar is a mad house from a driviing perspective. Vehicles go where ever there is a gap whether on the right or wrong side or the road, the side walk or nature strip. Also vehicles do ot stop for pedestrians even at pedestrian crossings controller by lights.