This short explanation may help.
Users (aka user records in /etc/passwd) must have a unique userid (aka uid) and each user must belong to at least one group.
See useradd/adduser cmds.
The trick in your case is to design and create the groups first (groupadd/addgroup cmds) and then create the users into those groups.
See /etc/group.
As noted, each user must have a 'primary' group (as seen in /etc/passwd rec), but you can add them (usermod/moduser cmds) in to multiple groups.
This info appears in /etc/groups as you add the memberships.
Last but not least, files (inc dirs which are files in Linux) can be accessed through 3 sets of permissions: owner (aka user), group, other (aka world).
Each of these eg user perms consist of a combination of r (read), w(write), x (execute for files, search for dirs) in that order eg
Code:
drwxrwxrwx # NB: 'd' is the file type; for a regular file its denoted '-'
# ie filetype user grp other
See the 'ls -l' cmd and spend some time reading up on all the cmds I've mentioned so far.
I've never really setup printers by group, but its likely do-able. I'm sure someone else will coma along and explain or you can try google.
Feel free to rtn here with more qns.
HTH & Welcome to LQ (I used to Admin Novell v2 & V3 back in the day).
PS: You can find plenty of manuals/books free to read online @
http://www.linuxtopia.org/