If you want to give permissions to some users who are in a special group (probably sudo) to use
sudo without asking password, you can do this simple in two steps:
First of all, you must add related users to group
sudo. For example we can add bob to group sudo:
adduser bob sudo
And after that type
visudo command and add or comment out following line:
%sudo ALL = (ALL) NOPASSWD: ALL
It says that password not required for the users who are in group of sudo.
Note: If you're not in the sudo group previously when logging into X session and added yourself into the group sudo, you need to logout from X and relogin to group membership changes take affect. If you're making this changes on a remote server through ssh, you need to logout from server and connect again.