I just installed Ubuntu 12.10, and I tried to install Eclipse and C++, but I failed miserably.

I started with an installation from the Software Center, Eclipse worked, but only in Java. Then I started googling for installation guides and tutorials, but after hours of downloads and installations, the C++ in Eclipse still doesn't work.

So now I have two questions:

1. How do I clean up this mess?
   Actually, how do I know if there is a mess?
   According to the Ubuntu Software Center, Eclipse is installed and has three add-ons.
   How do I know if the other installations of other Eclipse versions/packagings overwrote each other or if I have multiple installations?

2. How do I install the latest version of Eclipse and C++ in Ubuntu 12.10?

There is a package called eclipse-cdt in the Ubuntu 12.10 repositories, this is what you want. If you haven't got g++ already, you need to install that as well, so all you need is:

sudo apt-get install eclipse eclipse-cdt g++

Whether you messed up your system with your previous installation attempts depends heavily on how you did it. If you did it the safe way for trying out new packages not from repositories (i.e., only installed in your home folder, no sudos blindly copied from installation manuals...) you're definitely fine. Otherwise, you may well have thousands of stray files all over your file system now. In that case, run all uninstall scripts you can find for the things you installed, then install using apt-get and hope for the best.