In the My Time tab you can keep track of all the time you're exchanging with other sharers. You'll find all your upcoming shares in the "Coming up" section. An indicator will show you when one is starting soon, and you can tap to record the start time. You can also send a message to the other user from here if you need to check on anything before starting the task.
You can also see all the tasks you've provided or received in the past in this tab.