Hi Stefan,
first of all. It depends. The Instagram API with access to insights and all the cool stuff is available for instagram business accounts, connected to the Facebook page. RestFB is supporting this and I'm about to add some examples in our documentation. I didn't had enough time to add the examples so far. Maybe I can manage it this weekend.
But in short:
You have to connect the facebook page with the instagram account in the Facebook Page settings on Facebook.
Fetching the page data with the page access token allows you to access the instagram_business_account field.
With this information you can start fetching media, comments, stories and insights for this instagram account.
Hope this helps a bit.
Best Regards
Norbert