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As you've probably already figured out, creating groups is the way to share access to files on the Linux system. However, for a complete file-sharing environment, things are more complicated.
As you've already seen in the “Decoding File Permissions” section, when you create a new file, Linux assigns the file permissions of the new file using your default UID and GID. To allow others access to the file, you need to either change the security permissions for the everyone security group or assign the file a different default group that contains other users.
This can be a pain in a large environment if you want to create and share documents among several people. Fortunately, there's a simple solution for how to solve this problem.