There is a software program you can get online for Mongolian called Before You Know It. It is similar to rosetta stone and starts at the total beginner level. It's good for memorizing vocabulary and listening practice and it's not overly expensive.  Colloquial Mongolian, published by Routledge, had good explanations in English of the grammar and an accompanying CD. There is a book called Modern Mongolian: A Course Book which is way more dense and detailed but perhaps pricier and harder to get. It is good for reading/writing and getting really in-depth with the grammar. You could perhaps start with the other two first.

Thanks, -MacKensie

Hi, I'm Mongolian native speaker, but now I'm studying English. Maybe we can exchange our speaking skills. /Mongolian and English/