There is a huge demand for "Native" English speakers as English teachers. Anyone who is interested in teaching English will have no trouble getting employment and a work visa through a school or organization. However, the pay is generally low compared to other countries. Though it'll usually be just enough for room and board plus a little extra.
Local English-language media are another source of employment for native English speakers, offering work as editors, proof-readers or photojournalists.
Volunteer work is available teaching English, assisting with charity work and joining archaeological digs. These jobs are easy to find and are very rewarding.
There are some language schools in the capital. The two most well known ones to foreigners are Bridge School and Friends School. Both schools offer group study classes or individual tutors. Also the National University of Mongolia offers courses (http://www.num.edu.mn/Def...) usually takes Westerners about 9 to 18 months before they acquire good conversational abilities in Mongolian. Speakers of the Altai-Turkic languages, such as Turks or Kazakhs, tend to pick it up quicker due to the similarities in grammatical structure.