Except for the happy exceptions of US-citizens (please check the embassy web site nevertheless), most citizens of the world need a visa to enter Mongolia. But also for the rest of the world it isn´t difficult to get a visa to Mongolia. Generally all it takes, is to fill out a form, pay a fee and you get your thirty days.
But then procedure varies slightly from country to country. Here links to the departments of Mongolian embassies in select countries: