We consider Ubuntu desktop >= 18.04 with gnome desktop. The DNS and network has envolved and many pieces online does not fit anymore.
Currently, the desktop network is controlled by NetworkManager, which is the service name also.
The configuration file is at the directory: /etc/NetworkManager/system-connections/. The important part is
[ipv4]
method=auto
The configuration part is persistent after rebooting. The temporary files which store the current setting is located at
/var/lib/NetworkManager.
All the above comes from the package network-manager.
Usually the user does not need to modify the configuration file by hand; The GUI program nm-connection-editor(comes from package network-manager-gnome) provides a useful interface to edit configuration file of NetworkManager. Notice that to make the changes appliable. We should restart the NetworkManager daemon in some cases.
The dns is controled by systemd-resolved daemon, which reads the configuration file resolved.conf. There are many files with the same name on the system. To refresh DNS after changing configuration of network-manager. This daemon can be restarted.