if you have the open source version the essential's are
su zimbra
zmcontrol stop (if you want you can check your processes to be sure they stopped)
copy, tar, etc the /opt/zimbra folder (and if you made links or mounts to the store, index, etc elsewhere backup those too)
Backing up and restoring Zimbra (Open Source Version) - ZimbraWiki
zmbackup is for the NE version:
CLI - zmbackup Network Edition Only - ZimbraWiki
now there are a few threads on backup scripts and ways to backup the open source edition live...but if your new to linux...probably a little over your head
regarding cold & hot, full and incramental backups of open source version:
Full Server Backup and Restore of “open source version”