I am running 10.11.4 on my mac mini that has a public IP I want to be able to connect to it remotely How can I set up my mini ?

Set up and use Back to My Mac - Apple Support

As already suggested by Linc or,

https://www.teamviewer.com/en/download/mac/

or, search Google for remote desktop Mac.

As Linc Davis suggests, the best approach is using Back-to-My-Mac (BTMM). BTMM should even work if you have a router between you and the internet.

Do you have a Public IP address assigned to your Mac and it is directly connected to the internet, or does your router have a Public IP address?

The reason I ask is because not all routers work well with Apple's BTMM. If you have problems with BTMM and your router, you might consider trying TeamViewer.com. BTMM will give you more functionality, such as screen sharing and file sharing over the secure BTMM connection, but if you cannot connect, TeamViewer.com can generally make it though home routes to give you screen sharing, and a limited way to transfer files.

There are other methods, but they start to get more complex or expensive.

And if screen sharing and file sharing are not what you want, please let us know.