Learn Survival Mongolian
Although there is currently not a specific Mongolian phrasebooks, Wikivoyage users have collectively created a free Mongolian phrasebook with the goal of making it possible for travelers to "get by" while traveling in areas where Mongolian is spoken.
Wikivoyage phrasebooks are available in many languages and each one varies in depth and detail. Most of the phrasebooks include a pronunciation guide, a general phrase list, information about dates and numbers, a color list, transportation-related phrases, vocabulary for shopping and phrases for eating and drinking. Some are even more in depth, and all are free!