Sorry to say this on the Silverlight forum! But, if you can, walk away from it and try not to look back. I liked Silverlight, I really did, but unless you need to support a legacy application, or a client/management will not budge on project requirements, you really should try and convert what you have to JavaScript.
Have a look at this:
ArcGIS API for JavaScript
If you need JavaScript help, try w3:
JavaScript Tutorial
Also, once you read through this, have a look at:
jQuery Tutorial
And this:
Dojo Tutorials - Dojo Toolkit
The ArcGIS JS API is supported by Dojo, so you should have an idea about it, but I threw jQuery in there as well since you should have an idea about this library, too.
And keep jsfiddle in mind, for prototyping:
Hello World Example - JSFiddle
Honestly, Silverlight should still be supported by Microsoft (security-wise), until 2021, I believe, but I wouldn't expect Esri to support it, and I would venture to say that before too long, IE will be the only way to run Silverlight.