How to edit a theme and not spoil anything?

Question

WordPress

There is a working site, they want to change its design. We downloaded the theme, now we need to edit it, customize something, transfer widgets. Here you can check how it looks.
I wanted to ask how this process is established by experienced craftsmen.
One of the options is to install WordPress locally and try it, but I would like to do it on the customer's data, because there are a lot of things there. To transfer basis dump to itself?
In general, I'm interested in how someone does this.
Thank you.

Answer 1

Use to edit the child-theme template: The page in the codex
A DB can be cloned and reconnected in wp-config.php