create your group and then give users "membership" in the goup.
This doesn't do shit for security, however. What it allows you to do is make filesystem permissions easier to manage.
For example: there are 5 people in your company: bob, mary, sue, tom and mark. bob, tom and sue are developers and they would like to have a directory to store all of their development data. mary and sue are also in charge of the books. They would like to be able to have a place to share accounting data and not worry about anyone else seeing what goes on in the books.
so you create two groups, coders and books. Then you give bob, tom and sue membership in group "coders" and sue and mary membership in "books".
Now create a /development and an /accounting directory. Change the ownership to bob.coders and mary.books, respectively. Change the permissions to 770 (rwxrwx---).
Now anyone who is part of the coders group can access the /development directory, and anyone part of the books group can get into the /accounting directory. If you're not part of one of these groups (or not root), you can't even list files in the directory.
This is a *very* simple example. You may want to visit a library and see if you can't locate a few introductory unix books or google around -- there is a lot of power in groups that any post won't be able to give all the info on.