Each time you add a new user to a group (e.g., when you use passwd to create a new user account), you need to edit the /etc/group file and add the user to the appropriate group entry.
For instance, if you have an existing group techies and want to add zeke to the group, change:
techies:x:101:michel,jim,sue
to:
techies:x:101:michel,jim,sue,zeke
You should do this at a time when you're certain no users or programs are trying to use the /etc/group file.