$ sudo groupadd testgroup
$ sudo useradd -m -g testgroup testuser
$ sudo passwd testuser
Enter new UNIX password:
Retype new UNIX password:
passwd: password updated successfully
$ su testuser
Password:
$ cd ~
$ mkdir only_for_testgroup
$ chmod 770 only_for_testgroup
$ ls -ld only_for_testgroup/
drwxrwx--- 2 testuser testgroup 4096 Aug  4 13:53 only_for_testgroup/
$ echo "some text" > only_for_testgroup/file.txt
$ su ubuntu
Password:

$ ls
only_for_testgroup
$ ls only_for_testgroup/
ls: cannot open directory only_for_testgroup/: Permission denied
$ sudo addgroup ubuntu testgroup
Adding user `ubuntu' to group `testgroup' ...
Adding user ubuntu to group testgroup
Done.
$ ls only_for_testgroup/
ls: cannot open directory only_for_testgroup/: Permission denied