If you already have a tool on a toolbar that displays the labels you would use the following code to find the command and just call ICommandItem.Execute to execute the command.
desktop.arcgis.com/en/arcobjects/latest/net/webframe.htm#2ffb7cab-820e-4581-970f-49c887108f87.htm
I don't recall any out-of-the-box commands that display labels. In my code I display the labels using IGeoFeatureLayer.DisplayAnnotation. This is mentioned starting on the following page.
Working with labels and annotation (ArcObjects)
http://resources.arcgis.com/en/help/arcobjects-net/conceptualhelp/#/Working_with_labels_and_annotati...