Currently, a 30-day tourist visa is easily obtained at any Mongolian consulate, consulate-general or honorary consulate.
Follow the following steps and requirements to obtain a Mongolian visa from your nearest Mongolian Embassy:

• One copy of visa application form is required for Mongolian visas
• State clearly travel dates
• A valid passport must be produced
• For a group visa the Consular Section needs only passport of a tour leader and the rest of the clients should provide the following. (nationality, sex, date of birth, passport number, date of issue, date of expire)
• 3 recent passport size photograph should be attached.
• Self-addressed and registered Envelope is required in case visa applied by post.

 
All visas, except transit, are issued by the Embassy. The normal time required for a visa to be processed is one week. But for a transit visa - 48 hours without any authorizations.

To get a visa for longer than 30 days, you must be invited or sponsored by a Mongolian, a foreign resident or a Mongolian company, or be part of an organized tour from a Mongolian or foreign travel agency.

If you absolutely cannot get to a Mongolian consulate, it is theoretically possible to get a 30-day tourist visa on arrival at Ulaanbaatar airport. To do this you will need an invitation from a Mongolian travel company. It's best that a representative from this company meets you at the airport on arrival to liaise with visa officials.

It is also theoretically possible to get a visa at the land entry points at Zamyn-Uud and Sukhbaatar train stations, though until this becomes common practice you are better off using this as a last resort only. For both land border visas and on-arrival airport visas you will need US$50 and two passport photos.

Polish citizens do not require visas for a stay of up to 90 days, Israeli and Malaysian citizens can stay visa-free for up to 30 days and Hong Kong and Singaporean citizens can stay visa-free for up to 14 days.

MONGOLIAN TOURIST VISAS
Standard tourist visas generally last 30 days from the date of entry and you must enter Mongolia within three months of issue. Visas normally take several days, or even up to two weeks, to issue. If you want your visas quicker, possibly within 24 hours, you will have to pay an "express fee", which is double the normal cost. If you want a tourist visa for longer than 30 days you will need to arrange for a travel agency to invite you. Your sponsor will need to know your full name; date and place of birth; country of citizenship; passport number, date and place of issue and expiry date; your date of arrival and departure; and a general itinerary. They must send your invitation to the Ministry of External Relations in Ulaanbaatar. If accepted, a copy will be sent from the ministry to your designated embassy or consulate, where you fill out a visa application form and hand over your cash. Try to get a copy of your invitation if possible.

If this seems too much hassle, remember that 30-day tourist visas are easily extendible by 30 days in Ulaanbaatar. The only snag is that you'll probably have to return to the capital to do this.
Multiple entry/exit tourist visas are usually only issued to foreign residents who do a lot of travel.
Mongolian honorary consulates can issue transit visas and non-extendable tourist visas but only for 14 days from the date of entry. Importantly, they often issue visas without requiring a sponsor or invitation. However, these visas are for entry only; they cannot issue normal entry/exit visas, so you will have to spend some of your precious time in Ulaanbaatar arranging an exit visa from the ministry.

MONGOLIAN TRANSIT VISAS
These visas last 48 hours (sometimes 72 hours) from the date of entry. This will only allow you to get off the Trans-Mongolian train for a very short time before catching another train to Russia or China. A single entry/exit transit visa cannot be extended. You will need to show the train or plane ticket and a visa for the next country (Russia or China).