Make the current state recoverable
Before changing a live site, make sure you have a usable backup and know how it would be restored. Keep a note of the active theme, plugins and important settings. Use a separate test installation to explore a new theme.
Understand the theme you are installing
Block themes use HTML templates and theme configuration files; classic themes use a different template structure. Read the package documentation and use the editor intended for that theme. Do not assume a demo uses the same tools as your existing site.
Review the complete site
Check navigation, article pages, forms, images and the smallest screen size you support. Remove unwanted demo content and verify links. Publish only after the essential journeys work with your own content.