Once an Event with Milestones starts you can start getting tokens to work toward its rewards. The Event Milestones will reward the player with a different reward each time you reach the next checkpoint of tokens amount.
Each event has a unique way to get tokens, so pay attention to its tutorial once it starts or hold the click on the token icon inside the event screen to see a tooltip teaching you how to get them.
Once you hit the minimum amount of tokens necessary for each milestone, you will be able to click on its claim button to get the reward.
Did you forget to claim the rewards and the event ended? No worries, after the event ended you can click in the event icon in your screen and get all the rewards that you did not claimed while the event was running.