If you are making a mapping app these days without providing the user the option to show their location, you've kind of missed the 21st century boat, so to speak. For years now, this has been a standard feature of Google and Apple's mapping technology. ArcGIS Runtime comes with everything you will need to display your current location and more:
Displays the current location
Let's look at the classes that you will need to use. First, LocationDisplay is a property of MapView. It contains everything you need to show the current location. Here's an example of how it is done:
<Window.Resources>
<esri:SimpleMarkerSymbol x:Key="NotMovingMarkerSym" Color="Red"
Style="X" Size="16"/>
<esri:SimpleMarkerSymbol x:Key="MovingMarkerSym" Color="Blue"
Style="Circle" Size="12"/>
</Window.Resources>
<Grid>
<esri:MapView x:Name="MyMapView">
<esri:MapView.LocationDisplay>
<esri:LocationDisplay
...