How do you break down user stories?

In my experience it usually goes something like this:

1. Product manager creates user story.

2. PM meets with engineers to discuss the story and answer questions.

3. Engineers meet to break down the story into engineering tasks. This usually happens in a live meeting where someone is taking notes in a google doc and then someone adds all the tasks to Jira.

How do other people do it? What works well for you? What are the problems you have with this overall process?