To view metadata for a geodatabase object in ArcGIS Diagrammer, simply right click and select View Metadata as shown below. Please note that not all geodatabase objects support metadata, for example, domains and subtypes do not have metadata.
After clicking View Metadata, a new tab is added to ArcGIS Diagrammer. By default the raw metadata XML is displayed.
In the Properties Window, you can select one of the ArcGIS Desktop metadata stylesheets as shown below. These stylesheets translate raw metadata XML into readable HTML.
This is what the Parcels feature class metadata looks like with the ISO metadata stylesheet.
To edit metadata of a geodatabase object select the object in the diagram and click the ellipse button next to the Metadata property in the Properties Window.
The ellipse button will launch the ESRI ISO Metadata Wizard.