You did not mention deleting the /etc/sudoers file, therefore I'll assume it still exists. To edit the /etc/sudoers file you need to use visudo. Issue that command as root or sudo depending on your present situation. There is also a man page for sudoers, man sudoers command should bring it up.
The man page is not so easy to read/make out, so have a look at this -->http://www.wlug.org.nz/SudoHowto
Another thing, there should already be an entry for users belonging to admin group in /etc/sudoers, if you want your new user to have same privileges as first one, add him/her to the admin group via your distribution's Administrative/Users_&_Groups application or via command line, you should not need to add an entry using his/her name in /etc/sudoers if they belong to admin group. If you want to limit this user to certain commands only, check the "Only allowing a user to run a particular command" in the sudohowto guide posted above.