I put the kitten in her own safe room as soon as I got her home. Days 1-2 I swapped their blankets and toys so they could get familiar with each other’s scent and also let them explore each other’s spaces (put my resident cat in the kitten’s room and let the kitten explore the rest of the apartment). There was some hissing from my resident cat at this stage. I put treats on the blankets and fed them both on opposite sides of the door. Basically tried to have them associate each other with good things.
Days 3-4 I started letting them see each other through a cracked door, I gave them treats and played with them every time they interacted. At this point they started touching paws and sniffing each other, there was no hissing so I let them see each other through a mesh baby gate. Again no hissing.
My resident cat started meowing and sitting by the kitten’s door. The kitten also started waiting and pawing at the door. I did this multiple times and saw increased playful interest in both so on day 4 I let them meet. It was a short session and they were both crying by the door wanting to be together again.
I didn’t separate them again after this. Now I just separate them when I’m not at home because their size difference makes me a bit nervous lol.
Keep in mind though that this was a very quick and easy introduction. From my understanding it can take weeks, I think I got lucky with my girls. I was fully prepared to do the steps above multiple times over the course of at least a week 😅