For standard unix permissions you must always consider, the owner (user/group/other), permission bits, and the umask. The combination of these things are what describe your effective rights, and the permissions of new items.
- chown/chgrp set the ownership.
- chmod set the permssions
- the umask is part of each users environment and depending on how it is set, it will remove permission bits.
So if you want to create a shared folder for a group you usually need to do something like this.
- Create a new group (projectgrp) and add the users to that group.
- Change the group ownership of everything under your project folder to projectgrp
- Change the permissions of all the folders to 2775
- Change all the files to 0664.
- Change the umask for all users to 0002
Of course there are other things you can do with ACLs that are a lot more complex for the sysadmin, but can make things easier for the end user.