Instagram is a photo sharing service, easily available on smartphones. More importantly, it is a popular social network playing a role similar to Facebook. Parents who restrict or monitor their children’s use of social media need to be aware of the social aspects of Instagram.
SafeKids.com offers the following helpful advice (link):
Like any social networking service, there are both benefits and risks — the main risk being that you might share something and regret it later because it jeopardized someone’s privacy or embarrassed you or others — which is especially easy to do with a smart phone camera.
Talk with your kids
Parents should talk with their kids about whether they’re using Instagram and, if so, what they’re doing with it. You might want to ask your child if he or she is familiar with the privacy settings and have a brief talk about the appropriate use of photo sharing. Try to make it a conversation rather than a lecture and if you’re not familiar with Instagram, see if your child can explain how to use it — it might be fun for you too.
By default, anyone can follow you on Instagram and see your pictures and comments but you can configure it so you to approve future follow requests. To do this…
Read it all here: link