I was wondering if it's possible to write Firefox extension using .Net Framework? Had anybody such experience in writing Firefox extensions using C# programming language? Any good sites or guidelines would be very helpful.
Here is an example of what I need. Extension to enter phone number and to send SMS Message. I draw it in Paint, so I'm sorry for having no artistic touch.
Firefox extensions are written primarily in Javascript. See here: http://www.rietta.com/firefox/Tutorial/backend.html. So unless you can find a way to convert C# code/.NET Framework objects to Javascript, you are out of luck.
Assuming you're asking about writing an extension (and not a plugin), the best place to get started is with the info at the Mozilla Dev Center.
Konamiman is correct: extensions are mostly XUL (an XML grammar) and Javascript, packaged into a ZIP file with the extension .xpi. The various links from the page I linked should answer basic questions, like the one you posted above:
https://developer.mozilla.org/en/Building%5Fan%5FExtension
https://developer.mozilla.org/en/Extension%5FFrequently%5FAsked%5FQuestions
I'm not sure how you'd do for C#, but you can use XPCOM to call native code libraries: that's how the Glasser extension, for instance, is able to use the Windows-specific Aero effects.
IBM hosts a very good XPCOM tutorial at DeveloperWorks.
As has been observed by other respondents, Firefox extensions are primarily written in Javascript: but you're in luck, because Script# is a free tool that enables developers to author C# source code and subsequently 'compile' it into Javascript.