Out of the box, Jira tends to use very open permission schemes for Projects. You can see this by the default scheme which users the term 'Any logged in user' a lot. What you will need to do is to create a few new permission schemes to use in your projects. Steps on how to do this are in Managing project permissions.
For your projects, we tend to recommend that you use project roles to define permissions, and then add users to those specific project roles. If you have never done this before, I would also recommend checking out the KB JIRA Permissions made Simple
It attempts to help explain how Jira handles permissions and guide you in best practices for managing which users can access with projects.
While you are setting this up, it might also help to check out the Jira Permission helper. This is a utility built into Jira to help Admins better understand exactly what settings are in place in your Jira that allow or deny a user access to a specific action in a specific project.
Let me know if you have any followup concerns about this.
Andy
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