You can make labels for points, but not lines or polygons. So the workaround is to get the label point for the polygon/line, then create a new point note at that location, label it, and set the symbol to transparent. You then have labels.
For example -
Point myPoint = myPolygon.Graphic.Geometry.GetLabelPoint();
Note myLabel= new Note("Label", myPoint );
myLabel.Graphic.Label = "My Label Text";
myLabel.Graphic.LabelVisibility = LabelVisibility.Visible;
myLabel.Graphic.Symbol = ESRI.ArcGISExplorer.Mapping.Symbol.Marker.Transparent;
ESRI.ArcGISExplorer.Application.Application.ActiveMapDisplay.Map.ChildItems.Add(myLabel);