Firstly, open the in-app Settings, by tapping the ⚙️ in the top-right corner, and then select the Notifications & Alerts entry.
There, you'll first have to Allow Notification to receive notifications (maybe you already have). Afterwards, you can customize the default alerts you want to receive, set the time you would like to be reminded about all-day tasks (see Create all-day tasks) and choose a nice notification sound. To learn more about setting up alerts to your liking, check out Customizing alerts.
If you are not receiving notifications, make sure to check out Troubleshooting notifications.
Completing tasks from the notifications
If you press and hold on a notification, a small menu will pop up.
There you have the option to either edit the task or mark it as complete, right from the notifications.
Completing a notification will not open the app, and you can get right to your next task.