"Now I am connecting the dots on this story."
"Now I am connecting the dots of this story."
With the first, you have learned all the facts and hints, and you solved the puzzle (the story).
Then, with the latter it´s suggested that you are in the process of doing so. You are in the middle of finding the relationships between said fact and hints (on a one-to-one basis).
The former - focus on the end result, the latter somehow emphasizes the process.