The task is to make one user member of a common group, and make this group the default for this user. So, let's say we have the user binladen and a group alqaeda. First, find the group ID of this group by running grep on the /etc/group file:

$ grep alqaeda /etc/group

So, the group id is 777. Now, use the usermod command (as root) to include binladen in this group (and also his in is own user name group) and set the default to 777:

usermod --gid 777 --groups alqaeda,binladen binladen

All files created by binladen, will now get ownership binladen:alqaeda, with 644 as default access. If you'd like to set the default permission so that other group members can also write to new files, i.e. 664, use the umask command:

umask 002

To test it all, log out and back in again to make the changes apply, set the umask (you might want to included it in your ~/.profile or ~/.bash_profile script), create a new file and run ls:

$ touch test
$ ls -l test
-rw-rw-r-- 1 binladen alqaeda 0 Sep 11 10:00 test