I was under the impression that Ubuntu came with a bunch of software.
However, I went to the Software Center to see if a C++ compiler was available, but I didn't see one listed; there was only, "Calculator", "Text Editor", etc. And I see the LibreOffice products.

What is the recommended C++ compiler for Ubuntu and where do I find it? If it is already here, what am I overlooking, since I don't see it?
(I just installed Ubuntu 13.04 and am running it from a USB drive.)

The standard compiler is called 'gcc' and you can easily install it with:

or to install it along with several other helpful development tools:

"helpful" might be understating that. Installing gcc on its own is typically useless. You need some other things to make gcc useful. It is possible to figure out and install exactly and only what you need for some specific use of gcc (which will likely still be more than just gcc itself). But it is a lot easier to install build-essential and get everything you need for many typical uses of gcc.

I would say "helpful" almost to the point of being "essential"

The build-essential program set contains only the command line utilities. You will also need to install the graphical tools if you expect an IDE of some sort.

This one will do the trick nicely: http://www.youtube.com/watch?v=dnUTktvF21c

Another thing:

I kind of hinted at the fact that there are many IDEs that you can choose. Search for them as IDE in the software center. However, it will also find unrelated stuff (being your search query such a short string).

A short, non exhaustive list of IDEs is:

* Eclipse
* Netbeans
* Geany
* Code::Blocks
* MonoDevelop
* Anjunta IDE
* CodeLite
* Monkey Studio IDE

And that is just a few of the ones available through the software center, which not all are.

I recommend that you also look into installing Glade 3 or even 2. These will provide you with a graphical UI designer. However, Glade already is a prerequisite to installing a few IDEs, and they all support it.