Note: To use Adobe Fonts you will need a Creative Cloud account. Unlike Google Fonts, this is not a free service.
To begin using Adobe Fonts, navigate to Fonts Plugin → Adobe Fonts.
First you will need to add your API key to connect Fonts Plugin to your Creative Cloud account.
You can retrieve your Adobe Fonts API Key here: https://fonts.adobe.com/account/tokens
Once you have saved your API key your "kits" will be retrieved. By default they will all be enabled by default, simply click disable to remove any you don't need.
By default all kits will all be enabled, simply click 'Disable Kit' to remove any you don't need.
Your Adobe Fonts will now be available to use in the Customizer and Post Editor. There's nothing else to do.
If you add, remove or edit a Kit in Adobe Fonts, press the 'Refresh Fonts' button under Fonts Plugin → Adobe Fonts to ensure the most recent data is available to Fonts Plugin.