If you new in Ukraine and looking for long term housing you have to know some list of recommendations presented below.
First of all about legal features of rental housing.

The properties such as apartments for rent, houses for rent or rooms for rent can be rented by foreigners. You have to make sure that the landlord is a real owner. If you acting without lawyer or trusted real estate agent at least you can do is to check the documents of the landlord to make sure that he is a real owner and has a right to put his property for rent. How to check the landlord? Every true owner won’t mind to show his documents such as his passport to identify him and documents that proves his ownership. Which docs can prove the ownership? Usually it can be an buy sell agreement where must be written that the landlord bought the property he want to put for rent sometime before from seller. Also it can be a testament which proves that the landlord got the property from his family. These are most common docs of ownership, however sometime there can be some different ownership docs. In that case better consult with a lawyer.
The most important thing that the name of the landlord must be same in all docs he presenting. Also better check only original docs, not copies.
Thus, you will be sure in your landlord. In case the landlord will try to hide his docs there is reason not to trust him.
So, if you checked all the docs you can put a rent agreement between you as a renter and landlord as a lesee. The full features of rent agreement and it legal regulation you can read in “this article”.
Second, about real estate agents.
Most foreigners prefer to use services of real estate agents. That cost money but it much easier to get housing. However beware of fake real estate agents who promise fine housing, take prepayment and cheat, without providing any housing at all. The usual practice of true real estate agents who provide rental housing is when you give them a request, they offering you available options, arrange appointments for you, accompany you on appointments with landlords to let you check the housing. Only after you’ll decide to rent the apartment they take 50% from rent. That is one time payment after you’ll get the key and put rent agreement.
Use these recommendations to find a good housing and take care.