I recently have taken in a cat that is about one year old.?

She was found in an apartment with food, litter box and a gallon of water but the owner had been gone for over a week. The maintenance men new I recently had one of my cats die and thought of me. I took her to the vet and she is good except underweight.I have placed her in my bedroom with the door open,her own food, water and litter box along with some toys....I have two other cats and would like to know if this is the right way to have her acclimate herself and all of the cats to get to know each other. I think she is traumatized but otherwise good. Am I doing it right to get her used to the new house? Thanks you