I don't understand unix users, groups, permissions, etc. For example, things managed by the
groupadd, etc. commands. How do all these things work?
It's all a method of granting various access to a file.
User is an individual user. Use this when you want to give one person and only one person access. Group is more than one user. Use this when you want to give several people access. Put them all in a unique group and set that as the group owner. Other is for anybody who isn't the user or group owner.
A file always must have a user owner and a group owner. Often each user will have a group named after them with only them as a member. This way you can have a file that is truly owned by a single individual.
The permissions are as follows
R and W are probably pretty self explanatory. X may be a little confusing. In some situations you only want certain users to execute certain programs. For example, perhaps you don't want regular users to execute
File permissions when listed are displayed as something like
Some common "gotchas"
This post - Unix / Linux: Beginner's Guide to File and Directory Permissions is a good intro.