There was a really great thread on the Xamarin Forms forum yesterday regarding taking screen shots of your mobile application. I thought I would share this information here to summarize the conversation.
From Outside the Application
Greg Shackles wrote a great article about using Xamarin UITest to generate screen shots using the built-in functionality of the testing mechanism.
Fredy Wenger recommends using SnagIt, which I also use for all of my screen shots, regardless of platform.
From Inside the Application
Daniel Hindrikes created a ScreenshotManager component to handle the work from within your application. This work is documented here.
Norman Macay also pointed us to a previous post about collecting screen shots for Android.
All in all, there are a variety of methods, you just need to select the one that works for you, given your situation.