Happy Camel operates out of the Chez Bernard Cafe (which is a great little cafe in itself). They organise various outings, the full extent of which can be seen at http://www.happycamel.com/.
The staff there was incredibly helpful. We just wanted to get out of the city and stay in a ger. We were given all the different options, and our trip was completely tailored to what we wanted, but we didn't pay for anything more than that.
A taxi soon arrived to take us out to the national park in which we would be staying, and the lady helping us even got the driver to stop off so we could buy food for the trip and take us to a pharmacy en-route. We arranged to be fed by the family we were staying with and to spend a day horse riding while we were out.
The entire trip cost somewhere in the region of $50 for food, accommodation, transport, and horse riding. It was a brilliant experience, and Happy Camels did an excellent job of sorting everything out for us.