When I was learning to incorporate Ext JS with ASP.NET at my previous position, I found the best way to learn it (aside from the documentation and examples) was just going thru the forums and picking up up sample code here and there from user posts.
Once you've learned the nuances of the client API (and their online documentation and forums have been excellent in this regard), it's then just a simple matter of having your ASP.NET code returning the correct JSON for Ext JS to consume.
I have a rather outdated ASP.NET MVC / Ext JS sample project that probably won't compile anymore (it was built with an early preview release of MVC) but you can probably still go thru the code to see how Ext JS interacts with the server side code.
Ext JS and ASP.NET MVC Sample Project