How do I properly publish my Perspective project and share it with users so they can view the dashboard?
When you launch the project from Designer it will open a browser window. Copy the URL and share it with your users.
Also, how can I configure or limit access so that only people in my organization can open and use it?
Most Ignition instances are inside a company firewall so they are only accessible to people inside the organisation anyway. If the gateway is exposed to the Internet or you need to limit access for other reasons then Ignition's inbuilt security will do what you need. As Daniel has suggested, start with the online training.