WinDbg is a Windows Kernel Debugger, which is a part of the Debugging Tools for Windows package (http://www.microsoft.com/whdc/devtools/debugging/default.mspx).
While it is a good debugger for Windows, especially when debugging crash dump files, the best debugger for C# code is its native Visual Studio Debugger. You can debug your C# code in a free version of Visual Studio called Visual C# Express, which is available for download for free at http://msdn.microsoft.com/vstudio/express/visualcsharp/