Daily Challenges are unlocked after Level 71 and appear on the righthand side of the screen on the main screen: 

The Daily Challenge invites players to complete daily activities to unlock puzzle pieces. As they are completed, the puzzle pieces emerge, and eventually complete a snapshot from one of Wordsworth's travels. 

Tap on the icon to open up the Daily Challenge screen to see what challenges await: 

As you complete your challenges, you'll see they are updated here, and you can see your progress. In the image below, we see that one challenge has been completed in the puzzle piece, and another one is ready to be claimed: 

As you claim your rewards, you'll see your puzzle pieces put into place. Once you've completed a puzzle, it will turn into a poster, which you can then find in the Library of Lost Words, under "Gallery": 

Posters are updated monthly, so you have one month to earn enough puzzle pieces through Daily Challenges to complete your puzzle. If you haven't completed it by the end of the month, you won't be able to put that particular poster into your gallery. 

Once you've completed all of your Daily Challenges, you'll be informed of how long you need to wait until the next challenge is available: 

NOTE: If you are given a Daily Challenge asking you to "Inscribe" a certain number of words, please note that you to Inscribe words, you must go into the Library of Lost Words, open up a book with found Lost Words and manually Inscribe them. For more information, please visit our "Inscribing Lost Words" FAQ.