I haven't worked on Sharing Rule Before can anyone please help me.
So this is high time you start learning about Sharing Rules. A good place to start is the trailhead and reading through the documentation. You will find lots of resources on how to get more information about Sharing Rules.
As for your question, and assuming the "Share" checkbox is a custom field on your "Story" object, your best bet here is a criteria based sharing rule.
Criteria-based sharing rules determine whom to share records with based on field values in records. For example, let’s say you use a custom object for job applications, with a custom picklist field named “Department.” A criteria-based sharing rule could share all job applications in which the Department field is set to “IT” with all IT managers in your organization.
I will recommend, take a look at how you can configure the rules, build those and test it out. Hope this helps.