When we first got our new kitties (now cats) Emma, while playing with her toys, began to bring one of them to me. It was a small size "crinkle ball" made of felt interlaced with plastic mylar.
I decided to reinforce her behavior and would toss it to see what would happen. Sure enough she ran after it and brought it back to my general vicinity.
By not reciprocating unless she dropped it right in front of me, I hoped she would learn to bring the toy back to me and sure enough she did.
I started putting my hand out where she usually dropped the toy and sure enough she began dropping it into my hand.
Next we had to generalize her fetching behavior to other locations. The usual spot was while I was sitting on the chair in the living room with her return delivery to my hand after she jumped up onto the ottoman in front of my chair.
So when she would bring me the toy and drop it in my hand, I would go into the bedroom, her following, and toss it from there. In the beginning she would return it to the ottoman but eventually jumped up on the bed to return it to me for the next tossing.
Once she brought the toy to me while I was sitting at the kitchen island counter. She stood up on my leg with the toy in her mouth. I reached down, retrieved the toy and tossed it. Now and then she will bring the toy to me while I am using the toilet. I toss it.
By now she will fetch from any room in the condo and return it to my hand.
Once the little krinkle ball disappeared. I tried having Emma fetch the large size krinkle ball but she would have none of it. I trimmed the large ball into the same size as the small one and we were back in business. I since have purchased half a dozen more small krinkle balls.
Recently Emma has begun to generalize her fetching behavior by bringing me toy mice to toss. She has two or three (out of dozens) favorite mice that she will bring to me.
I might add that she screams in a very loud voice while playing fetch. I think she thinks that she is killing the animal and bringing it back to me to show off, which cats often do.
Either way I am not sure whether I have taught Emma to fetch or if she has taught me to toss?