How many countries are not a member of UNO what are they?

There are three nations not a part of the United Nations:

Vatican City

Taiwan

Kosovo

Vatican City has chosen not to be a part of the UN, however, it is an observer state. In 2004, Vatican City was granted all the rights of a member state, except voting and putting forward candidates.

Taiwan used to be widely recognized by many countries. However, since it is in a state of dispute with China, in order to be an ally of China you must not recognized Taiwan. This is why Taiwan is virtually unrecognized today, or at least by many Western Nations. Taiwan was a member of the UN until 1971, when it was replaced by the People's Republic of China.

Kosovo also lacks the amount of recognition needed to be a member of the UN. It is just a couple of recognitions short of having 50%+ of the members of the UN recognize it as a sovereign nation, as at least half is needed. Many Western countries already recognized Kosovo, and a few more might recognize the country soon (such as Spain and Greece).