Run in a terminal:
sudo visudo
The sudoers file will be opened with your default editor. There add this line at the end of the file:
sudoers
username ALL=(ALL) NOPASSWD: ALL
Then save and exit.
If you misconfigure the sudoers file you may end up in a situation where you wouldn’t be able to use sudo. This could be easely fixed by just using su to became root and then fixing the sudoers…
sudo
su