public void ShowCustomPopup( 
   IEnumerable<PopupContent> popupContent,
   IEnumerable<PopupCommand> commands,
   bool includeDefaultCommands
)

public void ShowCustomPopup()
{
  //Get the active map view.
  var mapView = MapView.Active;
  if (mapView == null)
    return;

  //Create custom popup content
  var popups = new List<PopupContent>
        {
            new PopupContent("<b>This text is bold.</b>", "Custom tooltip from HTML string"),
            new PopupContent(new Uri("http://www.esri.com/"), "Custom tooltip from Uri")
        };
  mapView.ShowCustomPopup(popups);
}

public void ShowCustomPopup(MapMember mapMember, long objectID)
{
  //Get the active map view.
  var mapView = MapView.Active;
  if (mapView == null)
    return;

  //Create custom popup content from existing map member and object id
  var popups = new List<PopupContent>();
  popups.Add(new PopupContent(mapMember, objectID));

  //Create a new custom command to add to the popup window
  var commands = new List<PopupCommand>();
  commands.Add(new PopupCommand(
    p => MessageBox.Show(string.Format("Map Member: {0}, ID: {1}", p.MapMember, p.IDString)),
    p => { return p != null; },
    "My custom command",
    System.Windows.Application.Current.Resources["GenericCheckMark16"] as ImageSource));

  mapView.ShowCustomPopup(popups, commands, true);
}