How do I get a residency permit?

You first need to submit a request for a residence permit to the Ministry of Foreign Affairs, or to the Montenegrin Embassy or Consulate abroad.

A Temporary Residence permit can be approved if the foreign citizen wants to work in Montenegro, study, or join their family. There can be other reasons that are determined by the Montenegrin and/or International laws. A temporary permit lasting up to two years can be issued, as long as the foreign citizen submits  proof that he/she can support themselves, has health insurance (from the country of origin), and he/she has a valid reason to apply for a residence permit. Also, proof that the person applying for residence has not been criminally prosecuted has to be submitted.

Permanent residence is approved if the foreign citizen has spent more than 5 years in Montenegro (with a temporary permit), has been married to a Montenegrin citizen (or to a foreign citizen who has permanent residence) for more than 3 years, has Montenegrin origin or is a child or close relative to a Montenegrin citizen or to a foreign citizen who has permanent residence in Montenegro.

There is some brief information on obtaining residency permits at  http://www.mvpei.gov.me/en/sections/consular-affairs/visa-regimes-for-foreign-citizens/