How to update a theme (and childtheme) without changing my own settings I did in the childtheme

Hello, since 3 month, my website is online. In this time, I’ve got 3 emails to update the sporttheme I’ve bought.
I red here in the forum, that I have to use only the latest update. ok.
It is written, that I have to download the whole package. And after that, what should I do then?
Should I delete the active theme first, then doing the upload. After uploading activate the theme?
What is the right order? Besides I use the childtheme of the theme.
Or should I upload the new theme (two uploads: theme and childtheme)
Then active the new childtheme or at first, the new theme and afterwards the new childtheme …
I made some modifications in the styles in the childtheme. Therefore I’m scared about the update.

Thanks for your help. I am new and I don’t know, what happens, when I start the upload respectivley the activation of the theme.