I assume you've read the Online Help about using extensions: Manage Dashboard Extensions in Tableau Online - Tableau
Your questions aren't very clear, Brian: what does this mean - Are there extensions which Tableau online customers can publish viewable to others in the company online (cloud). Do you mean publish a dashboard that CONTAINS an extension, or do you mean publish an EXTENSION to Online that others can use? The 2nd one is not how extensions work.
Users don't have to do anything to USE an extension if it's part of the dashboard they are using. It just works like any other part of a dashboard, like a filter or parameter.