In order to read a comic while your mobile device is offline, add that comic to your library by tapping the comic, then tapping the "Add to Library" button. Once a comic is added to your library, you will see an option to "Read offline?" Simply turn the switch to "on," and that comic will be downloaded to your device. You will be able to see all your comics for offline reading in the "My Library" section on your mobile app.
You may choose up to 6 comics at a time to read offline. Reached your max? Don't worry — you can always delete comics you've already read by going to the "My Library" section and clicking "Edit." Once you've deleted comics from your read offline queue, you can add more issues.