How do you install 3rd party apps on iOS 10?

Go to the App Store and download them.

If you have a profile on your device, it will show up. Such profiles should only be installed if they come from trusted sources such as your employer.

robnicol01 wrote:

The app I'm trying to install is not available in the app store. It is from a website where I download by clicking a link. When i do that, a dialog box pops up confirming the install. When I click yes, nothing happens.

You're lucky. What you're attempting to do is very unwise.

Since it is an app developed by your employer, you will need to address this with them to update the app to work with iOS 10. There is nothing we can do in this situation.

It will appear once you have installed the profile according to your company's instructions. It usually involves downloading the profile from their website.