This is the most basic scenario:
Once you have registered liber.io with your Google Drive account you will see a new option in your document's context menu:
You may need to re-log in into you Google Drive account to have this option activated. And of course you need a text document to export, which may use custom fonts and images, all of this is imported into liber.io ePubs.
After 'Open with' Google Drive will forward you to liber.io where you will see a landing page like this:
When writing you text make sure use 'Headline' format on the chapter and section headlines as liber.io will build the table of contents based on this formats.
After selecting your options liber.io will produce the ePub and store it in your Google Drive and your liber.io library. That's all it takes to create your ePub.