How I am doing it:

1. Make a copy of your whole webspace folder

So if your site resides in:

/var/www/vhosts/yourdomain.com/httpdocs

copy httpdocs and rename it to something else live 'version2'

2. In your admin interface (Plesk, cPanel, whatever), create a subdomain of your working domain that points to your new site:
Old site ->http://yourdomain.com

Tell robots.txt to not index anything or your subdomain will be received as duplicate content.

BUT BEWARE: With this method, both your old and new site are using the same database. You can do this if you want to simply change the theme and adapt the CSS, but everything in the filesystem! If you change the appereance through concrete5s front-end (Design-Dialog in Blockedit), these changes will also appear in your current site and might break the looks.

If you wanna go safe, you also need to create a new database for the 'version2'-site.

But over all this, you could also install concrete5 in a local environment on your computer (MAMP, XAMPP will help you), which is quicker to work on and totally independent from the web-version.

Thank you, Cahueya,

This is some good information.

May I ask what version of Concrete5 are you using? I need to update my site to the newest version and wondered if I should do the updates before the theme revision.

What are your thoughts on this?

At best I'm a self-taught techie which could be dangerous if I'm not extremely careful!