Americans and Israelis get 90 days automatically.
Most nationalities don’t need an Letter of Invitation, but check the internet for full details of who needs an LOI as things change rapidly.
You get 3 months from the date of issue of your visa to enter the country.
Embassies in surrounding countries:
It’s easy to get the visa here.
Flying out of Mongolia.
China: It is possible to fly to Beijing from UB but you will need a Chinese visa, available with a fair bit of trouble in UB. You will need hotel bookings, onward tickets etc. Ask other travellers or check the Thorn Tree for advice.
If they are too awkward then you can always fly to HK and get a visa on arrival and then apply for a Chinese Visa there. Travel agents in HK are very quick to organise Chinese visas of various lengths
Kazakhstan: It is also possible to fly from Bayan Olgii in the far West to Almaty in Kazakhstan, providing you have a Kazakhstan Visa. You can also get a visa on arrival but you will need a Letter of Invitation, available for a fee from Stan Tours (David is very efficient) for a fee. There are other companies but most are more expensive .
See the individual country pages for requirements.