Option 1: Download from Toodledo or Google

If you synchronize with either Toodledo or Google, then your tasks will automatically download to your new device when you install the app and set up synchronization.  If you synchronize with Toodledo, then your notes will transfer as well.  If you synchronize with Google, your notes will not transfer since Google does not support notes outside of tasks.

Note that this method does not copy settings and custom views, since Toodledo and Google do not support this type of data.

Option 2: Use the Backup and Restore Feature

The backup and restore feature can be used to transfer all data in the app, including settings, custom views, and notes (which cannot be stored in a Google tasks account). 

The first step is to make a backup on your old device by going to the "Backup and Restore" area in the app's settings.  From there, follow the instructions in Backup and Restore section (see https://utl.uservoice.com/knowledgebase/articles/92057).