Empty your mailbox and thoroughly clean the cover with the cleaning solution. Remove any grime, mold or dirt that can interfere with the primer's adhesion to the mailbox. Dry the cover with the rags.
Lay down a drop cloth below the mailbox, unless you don't care about getting paint on the sidewalk or yard.
Brush on one layer of primer to the entire surface of the mailbox cover. Let the primer dry for as long as is indicated on the packaging, and paint another layer if you note any of the original images from the vinyl peeking through.
Paint over the primer with whatever design you wish to display on your mailbox cover. Paint numbers and letters to show off your address, for example.