Always use visudo to edit the sudoers file. As when you use this and save the file it will check that you have used the correct syntax.
To set it up for one user without asking for a password, add this to your sudoers. replace USER with your users name.
USER ALL=(ALL) NOPASSWD: /sbin/shutdown
Then to shutdonw type 'sudo shutdown'
If you want to use sudo to do this then you will have to type sudo.
If you want to allow the group users to do this put this in your suduers.
$users ALL=(ALL) NOPASSWD: /sbin/shutdown
If you want to prompt users for there password to shut the system down remove the NOPASSWD.
One thing to point out is thatthe two above examples will let a user shutdown the system from anywhere, ie via ssh, telnet etc. To stop thatyou could use something like,
This will let everybody in the group users to only shutdown the system from the localhost.
I hope this helps and has not confused things any more for you.