I am experienced on Esri gis desktop and engine development.But i want to learn about the web side.Where should i start ? There is noone to teach me where to start.Is it as difficult as desktop and engine development.(p.s. i am using C#)
You should probably start with the interactive samples on the ArcGIS Resource Center:
This will give you an idea of the XAML and C# required to accomplish specific tasks using the Silverlight API.
I also recommend the Concepts link on the same page, which will give you step by step directions for writing code with the API.
If you are experienced with desktop esri development, moving into the web APIs should be relatively painless. You mentioned c#, and esri does provide a .NET web adf, but I would stay away from that at this point. It seems less people are using it and support is slowly decreasing.
One area to keep a eye on with the ESRI JS API, they are starting to get more of the HTML5 goodness flowing. As you see this moving up you will see Flex/Flash and Silverlight start getting less flashy.
Since the HTML5 spec is geared towards a common layer without the plugins required to use. So for the time being Silverlight will be a good form, but don't bet the farm on it, even Microsoft has let it slip and then back-pedaled that it won't be incredibly long for this world.
Now on the otherhand WPF on the desktop is a different matter, but that isnt web driven with a runtime.