You are correct about what the compiler is.
Xcode is a program that is a powerful text editor(what you will write the code in) and can compile your programs with the click of a button. When you create a c++ file(.cpp) it should automatically open it using Xcode. I would start there, and use Xcode to edit your files, and then open up terminal and use g++ to compile them.
When you get into more complex programs that require multiple classes and files, then use Xcode to create a project, this is where you will be able to click a button and have it automatically build and execute. You could skip straight to this step, but it is important to know how to command line compile your program and it will help you understand it all better.
Xcode can be found under Max OS X->Developer->Applications->Xcode
If you do not have the developer folder it is because you have not installed it off of your Max OS X disk yet. Insert the disk and look around for the installer for the developer tools.