You need to be running at the minimum Snow Leopard v10.6.6 (v10.6.8 preferred) to have access to the App Store.
If you have Snow Leoaprd v10.6 installed, download and install the Mac OS X 10.6.8 Update Combo
If you are running Lion v10.7, download and install the OS X Lion Update 10.7.4 (Client Combo)
Either combo will reinstall the App Store for you. Restart your Mac after the combo is installed.