A long long time ago, the only way to install software on Linux was to build (compile) from sources, using commands typed in a console. Linux has evolved tremendously since. Major Linux distributions (distros for short) now offer user-friendly UIs to install software as easily as in Windows. On Ubuntu, the Software Center is the easiest, but it is limited to free and open source software. Commercial apps are not available (but this soon may change, since the Ubuntu 10.10 release, coming October 10th will offer a commercial software repository).
On Ubuntu, programs which are not part of the official repositories can also be installed effortlessly in an UI called the Package Manager, provided they are supplied as Debian packages. These are file archives with the *.deb extension. A double click on the downloaded file will launch the Package Installer. All that is needed is to click on the "Install Package" button, then enter the system password, and the package will be installed with no further step.
Unfortunately, on Ubuntu 10.04 64 bits, ARES Commander Edition won't install this way, because Graebert has not provided a 64-bit package, only a 32-bit one. I get the following error shown in the screenshot, and you can see that the "Install Package" button is inactive.

Force installation of the 32-bit package on Ubuntu 10.04 64-bit
To install 32-bit software on Ubuntu 64-bit, you need to install the ia32-libs runtime libraries and the util-linux package. (Both links are based on the apturl protocol: simply click them to install the packages directly from your browser. Ain't that cool?)
Then, we need to use the terminal (available through the Applications > Accessories > Terminal menu). Enter the following command:
sudo dpkg -i --force-architecture [package's name]
Where [package's name] should be replaced with the file name (without brackets), including the complete file path. But here's a tip: instead, from your file manager window, simply drag & drop the file on the terminal window: the complete path with file name will be added automatically.

You then only need press Enter to execute the command.
As a rule, I dislike using the terminal, and I think that too many blogs and forum posts use terminal commands to install software or do other tasks. It gives the idea to people unfamiliar with Ubuntu that entering commands in a console is mandatory. This is not the case! Most of the tasks can usually be done using a user-friendly interface. But in this very specific case, I wasn't able to find one.
Tip based on the Ubuntu-fr French Community's Documentation.