You may have been to YouTube and noticed the Linux videos that show off the desktop effects. For the most part what is seen is rather amazing because other operating systems don't quite have the eye candy that are seen in these videos. Many people get excited at the visual effects and download a Linux distribution only to find that they have no clue where these visual effects are and how to turn them on.
Firstly it depends on your distribution and what it comes installed with. You will need to find a program called Compiz Fusion and install it to your machine. If you are using Debian packages it will be in the package manager. Search for it and get it installed to the system. This is the basic program that you need to have some of the major effects that you are looking to use on your system.
Once it's installed you will need to run the program for it to be on. If you don't want it on all the time, only turn it on when you want those visual effects. If you want it on all the time, consider telling your computer to run compiz at start up so that it's always running.
In order for some the effects to work, like the popular desktop cube, it will have to be turned on in the Compiz Settings Manager. This is normally found with other System or Administrative programs. What this will do is enable a person to set which effects are on as well as keyboard shortcuts for those effects.
The graphical possibilities with something like Compiz are amazing, and it will take one more than a few hours to sit down and see everything that it does. Once you learn how it works, you can get your system to look exactly like the many videos you have seen before.