You start with a pair of grommet pliers (mine are by Dritz, purchased from amazon.com) and a package of grommets (purchased separately, as I wanted silver).
Now take a grommet 'washer' and place it over the post. The domed side of the washer should be facing up. (A spare post/washer set on the side there so hopefully you can clearly see the difference.)
Grab your grommet pliers, and turn the white platform around so the indented end meets up with the metal piece.
Time to press that grommet on! The large white part of the platform will protect the right side of your grommet on the top of your piece, while the metal bit will spread the post to keep the grommet in place. Press as hard as you can at this point!
While the front looks nice and finished like this: