I think the extensions/Robot.html sample shows an example of clicking.
If you are wondering where that particular button is, you can find it by looking the “Selection” Adornment associated with the selected Node.
First, find the Node that you care about. Maybe you’ll use myDiagram.selection.first() or myDiagram.findNodeForData(someData).
Second, find the “Selection” Adornment: node.findAdornment("Selection").
Third, find the button somehow, probably with: adornment.findObject("ButtonName").
Fourth, get the button’s center point in document coordinates: button.getDocumentPoint(go.Spot.Center).
Fifth, pretend to click at that point, as shown in: