To set up a new website in Adobe Muse, open the program and create a new document with specified page dimensions. Use the master page to insert elements like headers, footers, and menus that will appear on every page. Add the required pages to the site structure and export the completed document to a folder. The learning objectives are to understand how to open Muse, set up a new document, add pages that meet the brief's requirements, and export the finished website.