On Snow Leopard, you can't use AirPlay Mirroring, but if you upgrade to Mountain Lion, you will be able to use AirPlay MIrroring > http://support.apple.com/kb/HT5404
If you want to upgrade to Mountain Lion, first make a backup of your files. Then, open App Store and purchase Mountain Lion, and follow the steps to upgrade to Mountain Lion. Check if your applications are supported > http://www.roaringapps.com
If you don't want to upgrade Mac OS X, you can also install AirParrot > http://www.roaringapps.com
If you are referring to AirPlay on iTunes, you can do it. The AirPlay icon will appear on the iTunes toolbar when your computer detects the Apple TV