1. Leap Second Cloud backup
The recommended way to back up your journal is to upgrade to Pro and enable cloud storage.
Once you upgrade to Pro follow the next steps to turn on cloud storage:
Enable cloud storage (Pro)
Edit your journal and tap "enable cloud storage".
Double check that the cloud icon does not have a slash through it. Once cloud storage is enabled you will see a cloud with no slash. It may take several minutes to back up your journal.
Create an account so you can access your account if you reset your phone or get a new device.
To restore your journal from cloud backup, log in to your account. Your journal(s) will automatically download.
2. Manual device backup
Manual backup happens outside of the Leap Second app and requires backing up your entire phone. Here's an article on how to backup & restore on a new device.
3. Photos app backup
Apple iCloud backup
If you're storing your journal in the Photos app, I recommend enabling iCloud Photo Library. You can enable it in your settings, Settings > Photos > iCloud Photos. This is a service from Apple and has a monthly fee. Your journal will be safely backed up once it is uploaded to Apple iCloud.
Manual backup
If you'd like to manually back up a journal that's being stored in the Photos app, you'll need to unhide your journal. There is a bug in Apple's iOS that prevents "hidden" photo albums from being backed up.
Select your journal from the dropdown at the top of the app and click the edit icon next to the journal's name.
Turn off "Hide content in Photos app"
Navigate back to the Photos app and make sure your album appears and all your videos are there
See section 2 above for instructions on manual device backup