Simply tap the Activity Overview on the top right, and select Monster Invasion  under the Get Materials tab as illustrated below:

You can choose the challenge level when you enter. Complete lower-level challenges to unlock higher-level ones.

You may choose to go in solo or team up with other players from your Camp.
You get participation rewards as long as you enter. Complete up to 3 stages to earn stage rewards for each stage.

In addition to directly attacking the monsters with your own character, you may also fill the cannons with the cannon balls, and bombard the monsters.