Using Obsidian Sync
The paid addon option lets you create 5 ‘remote’ vaults for you to use.
These are ‘end-to-end encrypted’ meaning they are private.
No one can get access. So DON’T FORGET YOUR PASSWORD!
Once you have a sync vault you can upload the files and folders.
This is just like a cloud service. Each change in your Obsidian will automatically be sent when you are online.
Syncing to mobile
The mobile version works the same. Turn on sync. Adjust the settings. Let Obsidian sync do its thing.
Phones do go to sleep after a while. If you enable the ‘prevent device sleep’ toggle, your phone will wait for sync to be complete.
Free sync options
A post in the forum goes into detail about options, alongside the page on the official Obsidian help.