Here's a really good FAQ
on Mongolian and Mongolia, it's got answers to questions like 'Is Mongolian easy to learn?', 'What kind of language is Mongolian?' etc.
If you can understand Japanese, there's a really good Mongolian course at TUFS Language Modules
. It's a video based course with loads of drills and exercises.
And if you want to study Monglian with audio there's another Peace Corps course
, not the same as the Peace Corps course mentioned before, this one mainly teaches you useful words & phrases with some dialogues.
Indiana uni also has A Student's Guide to Khalka Mongolian Pronunciation
available as audio downloads.
The Russian course that zhiguli was talking about might be this site
. It's got several Mongolian grammar books in Russian and one in Italian.Digital Dialects
and Funky Mongolian
have some short flash based tutorials for learning common words.
As for whether Japanese is related to Mongolian, I don't know whether it's related
but the grammar is quite similar. They're both agglutinative languages so if you already know Japanese before starting Mongolian you'll probably find it easier to grasp the grammar. My Japanese teacher once told us how in one of his old Japanese classes, one of the students was Mongolian, and he progressed much faster than the rest of the class.
I'm also interested in studying Mongolian, but not for a while. I'd like to visit Mongolia some day, so I would probably try to get a survival understanding of the language before I went. I got interested in Mongolian after I watched 'The Cave of the Yellow Dog', which is a really great film by the way. It's all in Mongolian and it's a really sweet story. 'The Weeping Camel' by the same directors is meant to be good as well.
And good luck learning Mongolian if you decide to take it up zhiguli! Let us know how it goes.