You have two options:

You can make another copy of Zen Cart in a different directory on your server, as long as you are allowed to have more than one database. This will be accessible from the internet, but only to those who know the path (e.g. www.yourstore.com/testshop/).

You can set up a server package on your home computer and do development work there. This is very convenient - no FTPing required to edit files - but will not be accessible from the internet, so you can't show others what you're doing. Also, depending on your computer and your site, it may run slow due to the heavy database use. See this article in the wiki > Customisation > More Advanced for full instructions.