Each user has a default set of permissions which apply to all files created by that user, unless the software explicitly sets something else. This is often called the 'umask', after the command used to change it. It is either inherited from the login process, or set in the .cshrc or .login file which configures an individual account, or it can be run manually.
Typically the default configuration is equivalent to typing 'umask 22' which produces permissions of:
-rw-r--r-- for regular files, or drwxr-xr-x for directories.
In other words, user has full access, everyone else (group and other) has read access to files, lookup access to directories.
When working with group-access files and directories, it is common to use 'umask 2' which produces permissions of:
-rw-rw-r-- for regular files, or drwxrwxr-x for directories.
For private work, use 'umask 77' which produces permissions:
-rw------- for regular files, or drwx------ for directories.
The logic behind the number given to umask is not intuitive.
The command to change the permission flags is "chmod". Only the owner of a file can change its permissions.
The command to change the group of a file is "chgrp". Only the owner of a file can change its group, and can only change it to a group of which he is a member.
WARNINGS:
Putting 'umask 2' into a startup file (.login or .cshrc) will make these settings apply to everything you do unless manually changed. This can lead to giving group access to files such as saved email in your home directory, which is generally not desireable.
Making a file group read/write without checking what its group is can lead to accidentally giving access to almost everyone on the system. Normally all users are members of some default group such as "users", as well as being members of specific project-oriented groups. Don't give group access to "users" when you intended some other group.
Remember that to read a file, you need execute access to the directory it is in AND read access to the file itself. To write a file, your need execute access to the directory AND write access to the file. To create new files or delete files, you need write access to the directory. You also need execute access to all parent directories back to the root. Group access will break if a parent directory is made completely private.