The Dream Wedding requires the goal Walk Down The Aisle!
You start by selecting two game characters, neighbors or Face Book friends you want to have marry. You can click the pencil icons next to their pictures to change who you selected and the person's status as Bride or Groom.
Send RSVPs to neighbors by clicking the Invite buttons at the bottom. To unlock more RSVPs you need to build more Wedding Buildings. Each one of those allows a different amount of RSVPs to be added. Most also require a decent number of building materials and must be completed, first.
You have 9 days to get as many RSVPs sent and accepted as possible (up to 160). The more you complete, the more the prizes at the end.
During the game, clicking on the Pink Cake icon to the right will return you to the Dream Wedding menu. You can also click on Show Me in goals like Walk Down The Aisle! when asked to 'Have RSVPs'.