See: http://codex.wordpress.org/Child_Themes#Using_functions.php
Specifics depend on what theme you are using and what you are trying to change.
I´m using Snapshot Theme from WooThemes.
I´ve edited the parent theme.
I´m trying to avoid customization loss.
You’ll need to ask Woo about that – these forums only support themes from the repository on this site.
There´s no customized code in “functions.php”
If you haven’t changed anything in the functions.php file, you should not have a copy of it in the child theme and you don’t need to worry about updating.
But always make a full backup of your site and DB before updating if you are unsure about things like this.