Hi Christine,
Here are some answers to your questions:
Which kinds of accommodation are available in Montenegro?
The Montenegrin market is typically a holiday market, offering mainly small size apartments, conceived for holidays. Very few 3+ bedrooms and villas on the market for long term lets.
Is it hard to find a flat or a house for rent in Montenegro?
It is therefore quite hard to find suitable accommodation for year-round living, as most properties were built for the needs of people coming on holidays with very small and basic kitchens, no proper heating system, bad thermo-insulation etc.
How to find a home in Montenegro: classifieds, real estate portals, real estate agencies?
Classifieds: for example in "tender oglasi" which has a section of accommodation. It is in montenegrin language so not so easy when you don't speak the language and many owners will also not speak english (for long-term look out for the word "duzi").
Real Estate Agencies: Only a few Real Estate agencies do long-term rentals (most agencies do only summer lets). The list is here: http://long-term-rentals-montenegro.blogspot.com/
How much is the rental for a house, an apartment?
The prices / per square meter / per month very from 6 (low quality) to 8-10 (average quality) up to 12-15 ; so a an apartment of 50sqm could cost 300 (basic) ; 450 (average) ; 650 (luxury) for example.
What are the formalities or the required documents for renting an accommodation?
Usually a lease is signed between the owner and the tenant and is then certified at a Notary office (which is necessary to have done when you are going to apply for a residence permit). Most owners require a 1 month security deposit. There is not much formalities otherwise, the market is not very mature, and it is rare to even do inventory lists for example.
Which advice would you give?
Ownership issues are not rare in Montenegro so it can be wise to use a registered agency who is checking this kind of details for you upfront.