"There is a big window in my room"
Translation:В моей комнате большое окно
Here's a set of declension tables for Russian non-reflexive possessive pronouns:
I wish there was an easier way, and maybe I'll figure out some short-cuts later on, but basically you have to pick the possessive pronoun which agrees in case, gender and number with the thing being possessed. It's a little easier with plurals, because gender is irrelevant to the pronoun being used - it's one pronoun for all plural genders.
For a declension table for the reflexive pronoun, see https://forum.duolingo.com/comment/29965925