There are a lot of different, yet still correct ways to manage stories in JIRA. It is generally accepted that a Story isn't complete until all its subtasks are done, it can still be useful to track progress of the subtasks. So here's how I do that today:
We divide all of our Stories in subtasks (technical/implementation tasks), and apply hour (time tracking) estimates to each of those. We estimate story points way in advance, then do more detailed estimating of subtasks and hours before starting each spring. During a sprint we use the hour/timetracking field as our more detailed tactical tracking field that stays day-to-day current.
Greenhopper then lets you view charts based on hours or points. So we use the point-based charts when looking at the overall project, but the hour estimate field for tracking our tactical progress in a sprint.
Hope that helps.