The config file /etc/sudoers lists the users who are allowed to run which commands as which user.
On Ubuntu, this file contains a line allowing all users of the sudo group to run commands as the root user.
To check which users are in the sudo group you can type getent group sudo. You can also check the groups of your current user by typing id.
To allow another user to run sudo, you can add them to the sudo group:
sudo adduser username sudo
Or, if your current user can't run sudo, you will need to boot into "Recovery mode" from Grub (hold shift while booting, if your grub menu doesn't show up automatically), or add single to the linux ... initrd ... quiet splash line, then:
mount -o rw,remount /
adduser username sudo
Run adduser for each user you want to be able to sudo. Then exit & resume.