You typically don't want to run as a root user because you can do a lot more damage to your system as root. Since root has ultimate power, you could accidentally delete an important system folder. In Windows you typically run as a super user also and have the ability to destroy your system (just go mucking around in the registry sometime).
The real problem for most people moving to linux is the idea of permissions. Most problems result from your user not having sufficient permissions to read or write or execute a certain file. Linux maintains permissions based on the user who created the file. So if your son created a spreadsheet under his account, you won't be able to read it by default because your login is different and those are HIS files. So instead, what you have to do is create and use group permissions to allow users to do common things or to share files. There are groups like cdrom and audio which you need to be a part of to use those parts of the system. At home, I have a common directory setup where my wife and I share documents and things like mp3's. But each mp3 has to have permissions that allow me to read it as well as her. Fortunately, there are ways to make sure every file that gets created in a certain directory has a specific set of privileges.
Anyway, the Ubuntu documentation is really pretty good and of course you can also ask questions here. So I guess I'd start at the Ubuntu docs.