It looks like this is a fairly popular interview question, particularly in junior or entry level .Net developer positions.

While there are tons way to do this, I am listing two common approaches.

• The most common way is string manipulation:

  string file = "abc.xml";
  Console.WriteLine(file.Substring(file.LastIndexOf(".") + 1));
  
  /// Returns xml
  

• .Net also has native class Path allows you to get file extension:

  /// Because Path.GetExtension returns extension ends with a dot, so you may want to get rid of it. 
  string file = "abc.xml";
  Path.GetExtension(file).Replace(".", "")
  /// Returns xml
  

Path also has a list of other handy file IO methods:

• ChangeExtension(string path, string extension)
• GetPathRoot(string path);
• GetDirectoryName(string path);
• GetExtension(string path);
• GetFileName(string path);
• GetFileNameWithoutExtension(string path);
• GetFullPath(string path);
• GetInvalidFileNameChars();
• GetInvalidPathChars();
• GetPathRoot(string path);
• GetRandomFileName();
• GetTempFileName();
• GetTempPath();
• HasExtension(string path);
• IsPathRooted(string path);

More details are available at http://msdn.microsoft.com/en-us/library/system.io.path.aspx