This is not easy. For me, I would go to group dining like Teppan Edo and Biergarten to be able to have a conversation with someone. At other restaurants I would look for another solo diner and ask them if they would like to eat together. Find someone that is not at the end of their meal. Sometimes, this would develop into spending the day with each other. I made conversation in ride ques, too.
When there were Disney conventions it was easier to join up with another solo to spend the day with each other. Sometimes, it would be for multiple days.
It can be hard to coordinate the time with each other like some want to be early risers and others are not. Not everyone enjoys the same rides. If you are willing to be more of a follower, it may be easier to be with a stranger.
I only did this a couple of times.