As an old-school Unix admin (started out on HP-UX 3.0), I use "real
root" all the time. Sure, there can be nasty consequences if you don't
know what you are doing or are not careful so I wouldn't recommend it
for a new user. I can remember back in the day, diving for the power
switch after inadvertently entering rm * . YIKES! On my servers, I do
most things with root. On my clients there is not any easy way to
become root.

Actually I don't know what being Root User is? It isn't when I log in from
Ubuntu Login is it. I seem to be able to get the software from Software Center
and Update the software from Admin. - this isn't Root User is it? Is Root User
only in Terminal? Like to know so I don't put my Ubuntu at risk.

Root User in Ubuntu is different from root user in a traditional *nix
environment. Basically root is to *nix what Administrator is to the Windows
world. Maybe this link will help you some?
http://en.wikipedia.org/wiki/Root_user

Ok I appreciate trying to lead me to the technical stuff -- but just because I
want to learn how to drive doesn't mean I want to learn how to take a car apart
and put it back together again.

In other words, I just want to know how to operate the Ubuntu Linux safely not
how to program it. I would be happy with going from Beginning to Intermediate
as I learn without even worry about the Advance part of it.

Again the Question is:

How do I know if I am a Root User or just a regular Administrator? I don't want
to be in the Root User but at the same time I do want to add programs from the
Software Center and Update the Software from the Updater program which I have
been doing. I don't understand the article they are very technical. I simply
want to avoid being in the Root User format that causes the security problems in
Ubuntu Linux. Now is the Root User something that is done in the terminal only?

You can't accidentally become root. You can only issue a command with
root powers if you use sudo on the command line, or a graphical system
administration utility asks for your password in order to grant you root
powers.

You can't make any system changes without root privileges. Which means,
you can't be removed from the administrative group and still be allowed
to make any changes on the system, including adding, removing or
updating software packages.

If you simply log in and do your work, browse the web, read/answer
emails etc, you are not using any root privileges and won't be unless
you do something that results in your being asked to enter your password
on the local system as part of the system administration authorization
process.

Well I am asked for password authorization when I want to install a program or
remove a program from Ubuntu Software Center and when I use the update software
program -- so am I in Root User then. But if so is it like Leslie Anne said
only for doing those processes of installing and removing programs from Ubuntu
Software Center and using the Updater Program and then I placed in a regular
user again format?

Yes, that is a fairly accurate statement. Keep in mind that ubuntu has a
root user, like all unixes, but the way ubuntu is set up by default,
nobody actually logs in as root. Instead, those who are in the admin
group are eligible to be granted root powers via the sudo command, in
order to make system changes.

No sudo, no root privileges. (note that sudo can be invoked for you by a
GUI but the tipoff is that you will be asked for your password)