First you need to create groups and assign users to groups. There are many GUI tools to do this, but they are different for each distro.
The command line tool for adding groups is "groupadd"
Then you need to set your folders to have group permissions. Use "chown" to assign group permissions to a folder/file: chown owner:group folder
Then you need to set the Directory Set Group ID so files created in the folder can be edited by the group.
Taken from
http://www.comptechdoc.org/os/...de/linux_ugfilesp.html
Directory Set Group ID
If the setgid bit on a directory entry is set, files in that directory will have the group ownership as the directory, instead of than the group of the user that created the file.
This attribute is helpful when several users need access to certain files. If the users work in a directory with the setgid attribute set then any files created in the directory by any of the users will have the permission of the group. For example, the administrator can create a group called spcprj and add the users Kathy and Mark to the group spcprj. The directory spcprjdir can be created with the set GID bit set and Kathy and Mark although in different primary groups can work in the directory and have full access to all files in that directory, but still not be able to access files in each other's primary group.
The following command will set the GID bit on a directory:
chmod g+s spcprjdir