Open the Professor's Experiments event window by tapping the lightning bolt icon in the bottom left corner of the screen next to the Friends button.
The experiments consist of tasks that you complete by performing regular in-game activities, like digging in the Mine, opening chests, earning coins, etc. You can find them in the Tasks tab.
There are two types of tasks. Daily tasks are updated every day at the same time, even if you're still in the process of completing them. Ongoing tasks are available at any time while the event is on, with new ones coming in almost every week.
Tap the task to see how you can complete it. All the tasks will be carried out automatically when you perform regular in-game activities. You don't need to accept a task to start working towards completing it.
You can claim your rewards in the Rewards tab. Complete Professor Verne's tasks to collect event points that will boost you along the rewards bar.
Rewards are divided into two groups. The rewards that are on the bottom row are free. The rewards on the top row are only available once you buy the Gold Pass. You can buy the Gold Pass at any time during the event. Once you buy it, you can collect any reward from the top row as long as you've advanced far enough along the rewards bar to claim it. Don't forget to tap Collect to claim your reward!
Perks are a special type of reward. You can only get them if you have the Gold Pass and can only use them while the event is on. Make sure to collect them as soon as possible to enjoy them longer!