How to implement a singleton in C#?

Singleton != Global. You seem to be looking for the keyword static.

If you are just storing some global values and have some methods that don't need state, you don't need singleton. Just make the class and its properties/methods static.

public static class GlobalSomething
{
   public static int NumberOfSomething { get; set; }

   public static string MangleString( string someValue )
   {
   }
}

Singleton is most useful when you have a normal class with state, but you only want one of them. The links that others have provided should be useful in exploring the Singleton pattern.