FYI some resources
Silverlight
(Website, about, tutorials, community) http://silverlight.net/
(Book) http://www.amazon.com/Accelerated-Silverlight-Books-Professionals/dp/1430224290/ref=sr_1_3?ie=UTF8&s=books&qid=1255333065&sr=8-3
ASP.NET Ajax
(Website, about, tutorials, community) http://www.asp.net/ajax/
(book) http://www.amazon.com/ASP-NET-AJAX-Unleashed-Robert-Foster/dp/0672329735/ref=sr_1_4?ie=UTF8&s=books&qid=1255332531&sr=8-4
ASP.NET + Silverlight
Since silverlight is just code embedded directly in the page, integration is pretty easy. However you can also get books giving you advice and best practices http://www.amazon.com/Beginning-Development-Silverlight-ASP-NET-AJAX/dp/1590599594/ref=sr_1_1?ie=UTF8&s=books&qid=1255332531&sr=8-1
BTW the Silverlight you want to be looking at is Silverlight 3. Additionally, Silverlight doesn't quite run on the full .NET framework. The runtime plugin is a trimmed down version of the .NET framework, that's about 4MB
Just had a quick read of http://computer.howstuffworks.com/silverlight.htm/printable
I turns out that Silverlight 1 uses javascript and Silverlight 2 can use other .Net languages such as C#. They both run on the .Net framework, which means you have @ your hands all the power .Net offers desktop applications.