Thanks for your question about moving your live site to your dev site. In order to properly answer that question we would need to know what type of site you're working on. If your site is using a system like WordPress, then it uses both a database and a set of core files that are typically kept in a specific folder. If you are working on a site built from scratch using only HTML, then you usually only need to concern yourself with the location of the website files. Note: If you installed the site with Softaculous (in cPanel), then it is possible to create a "staging site" with Softaculous. Follow this tutorial for more information.
If you could please provide details about the site you're trying to transfer, then we can provide more specific information. If you have any further questions or comments, please let us know.