I am using Ubuntu 18.04 LTS and the default desktop environment. I can't find /etc/X11/xorg.conf or /etc/X11/xorg.conf.d/ or similar files or directories. But, I can change the screen resolution, and the settings persist after I restart my computer. My question is: where does the system store the configurations of screen resolution set by a user? Are the configurations in a file somewhere?
You can check
sudo ls /usr/share/X11/xorg.conf.d/ there you should find a bunch of files corresponding to your current video drivers etc.
The second part of your question, regarding knowing what resultion to display: this will be dependent on your current desktop environment in use. One user can end up with different screen resolutions upon login if they have two different desktop environments like Gnome and XFCE installed for their Ubuntu distro.
For example, I use XFCE4 and mine is in
~/.config/xfce4/xfconf/xfce-perchannel-xml/displays.xml. If you use something else, you will likely find the display config file somewhere in your $HOME folder, for gnome if I recall correctly it
can be found by