I think you need to understand a bit more about how permissions work, because there a couple of ways they described or changed.
First, Every file has an owner and a group associated with it. Permissions are split into 3 sections - owner, group & public. Each of these can have a possible read, write or execute permission. These permissions can be expressed in character format or octal.
Here is an example of the character format:
[dave@cpe-147-10-189-254 ~]$ ls -ld Desktop
drwxr-xr-x 2 dave dave 4096 Jun 10 16:14 Desktop
I used the l option to get a long listing, and the d option bcause I listed a directory.
These are the permissions:
the d means it's a directory.
the next 9 characters show the permissions for owner, group and public.
the owner has read, write, execute permission for the directory.
anyone who belongs to the group has read and execute permission only.
Anyone else only has read and execute permission.
Now for the Octal part:
The permissions could be expressed in decimal
by allocating a 4 for read, a 2 for write, and a 1 for execute.
To make it easier they can be expressed in Octal
by adding them together for each of owner, group, public.
777 = read, write, execute for every one.
666 = read, write for every one but not execute.
So, rwxr-xr-x equals 755.
This shows that on my system the umask is 022 (for directories) because 777 - 022 = 755
One would use umask to set the default permissions automatically every time a file or directory is created.
chmod is used to alter the permissions after the file is created.
This shows that the owner is dave & the groupname is also dave. This where the user has their own group.
The reason why we have groups, is to make it easier to set permissions for lots of users at once. In a work situation, where you might have arhitects, engineers & planners, there would be a group for each of these, and each user would be placed in their appropriate group. Then, an administrator would set the group & group permissions for the directories & files nedded by a group. This way the admin can control access, so that for example, the planners can't get into the Engineers files & vice versa.
I hope that all this explains things clearly.