Here's a sample that registers a sample extension (.myext). A sample application (MyApp.Exe) is going to handle this extension. It also registers one default action as well as two other context menu operations. You may have to logout and login in after running this code to get the icon to show up correctly.

uses
  Registry;
procedure TForm .Button Click(Sender: TObject);
var
  R : TRegIniFile;
begin
  R := TRegIniFile.Create('');
  with R do begin
    RootKey := HKEY_CLASSES_ROOT;
    WriteString('.myext','','MyExt');
    WriteString('MyExt','','Some description of MyExt files');
    WriteString('MyExt\DefaultIcon','','C:\MyApp.Exe,0');
    WriteString('MyExt\Shell','','This_Is_Our_Default_Action');
    WriteString('MyExt\Shell\First_Action','','This is our first action');
    WriteString('MyExt\Shell\First_Action\command','',
        'C:\MyApp.Exe /LotsOfParamaters % ');
    WriteString('MyExt\Shell\This_Is_Our_Default_Action','',
       'This is our default action');
    WriteString('MyExt\Shell\This_Is_Our_Default_Action\command',
       '','C:\MyApp.Exe % ');
    WriteString('MyExt\Shell\Second_Action','','This is our second action');
    WriteString('MyExt\Shell\Second_Action\command',
       '','C:\MyApp.Exe /TonsOfParameters % ');
    Free;
  end;
end;