So, as far as I am concerned, this is the most concise and simple implementation of the Singleton pattern in C#.
http://blueonionsoftware.com/blog.aspx?p=c6e72c38-2839-4696-990a-3fbf9b2b0ba4
I would, however, suggest that singletons are really ugly patterns... I consider them to be an anti-pattern.
http://blogs.msdn.com/scottdensmore/archive/2004/05/25/140827.aspx
For me, I prefer to have something like a Repository, implementing IRepository. Your class can declare the dependency to IRepository in the constructor and it can be passed in using Dependency Injection or one of these methods:
http://houseofbilz.com/archive/2009/05/02.aspx