This sample demonstrates how you can take screenshot of a map. The app has a Screenshot button in the bottom toolbar you can tap to take screenshot of the visible area of the map. You can pan or zoom to a specific location and tap on the button, which also shows you the preview of the image produced. You can tap on the X button or any where on the preview image to close it.
How it works
AGSMapView has a method called exportImageWithCompletion: that provides an image depicting the current map display.