In previous versions of Ubuntu, you had to use different tools to install single packages that you’ve sourced yourself or that you’ve acquired from somewhere else on the Internet in the form of a deb file.
Now, the recommended and default method is to use the same Ubuntu Software Center that you use to install supported applications.
As an example, you can install VirtualBox, the virtualization software from Oracle. Go to http://www.virtualbox.org/wiki/Linux_Downloads and select the download for your version of Ubuntu.
Choose to save the file to a local directory, which by default is the Downloads folder. When you right-click a deb file, the default option is Open With Ubuntu Software Center. Select this option and you will be taken to the details of the application, where a message will warn you to install this package only if you trust its origin. In this case you can, so click Install.
If the dependency packages are not available in the repositories, the Install button is inactive, and the missing dependencies listed. In theory you must now source the missing dependencies manually, but it is very likely that, if they are not available in the repositories, the package in question just isn’t intended for either the version of Ubuntu you’re using, or even for Ubuntu itself (it might be a package designed for a different derivative of Debian, for example, or even Debian itself).
If, on the other hand, the software package exists on the standard repositories, Ubuntu Software Center will recommend that you install it from there instead of from an untrusted software source. If that is the case, it is wise to follow its advice.