Take everything you learned about the first part of this event and forget it.

Once you get through some quests and are asked to build the Elf Cannon, the event proper kicks off. If you had a chance to play yesterday, you should have already completed this phase. All you’ll be doing is tapping on elves, which turns them into Elves in Bottles. These represent your ammunition for the cannon. When you fire the cannon, you get Elf Bells. These are what you need to earn prizes. You can fire the cannon three times before it needs to cool down.

Visiting friends and tapping on their buildings gets you Elf Bells. Do this often, as it will help you earn prizes much quicker. If you can manage to tap on their Elf Cannon and/or Elf Cave you a get a few more bells than you would by just tapping a building.

Once you unlock the building shown on the right (the second prize), elves will also start dropping cogs which you can use to upgrade your cannon. This works very similarly to the Clash of Clans system of upgrading your castle. For the specifics of how that works, as well as what each upgrade does, here is a chart.

tl;dr

build cannon tap elves, get bottles fire bottles from cannon, get bells visit neighbors, get bells more bells = more prizes tap elves (after second prize), also get cogs use cogs to upgrade cannon better cannon = more bells