I'm not sure I understand your starting point. Do you have a bare fairway and green, neither of which are part of a relation? That is where you should be starting. If the relation already exists, I'll have to learn how the iD editor can modify that.

So, let's assume you draw an area for the fairway and an area for the green. When you are done drawing the fairway area, set it's feature type to Fairway. Draw the area for the green and set the feature type to Putting Green. Then hold down shift and make sure the fairway and green are selected. Right click on either selected line and click the "+" icon to "Merge" the features into a multipolygon relation. That's all you need to do.