Practically all programs that your run without admin privileges store their
settings in files in your home folder. Those files are usually either named
with the name of the program or are in directories with such names.
I haven't used Compiz, but you can search for files/directories '*compiz*' in
your home folder and delete them. I'm pretty sure that this will reset your
configuration. You can search like this in a terminal:
find -name '*compiz*'
Then remove directories and files you find. After that, logout and login.
> I'm not really familiar with Compiz although there is an a purge option
with apt-get that in theory should remove the configuration files.
This will only remove system wide configuration files, not user settings.
Those are stored in /etc, not in the home folder. For most programs this
won't reset user settings.