The Mac App Store is available as a free software update for Mac computers running Mac OS X v10.6 or later. If you have an earlier version of Mac OS X, you will need to upgrade to Mac OS X Snow Leopard.
Click the Apple icon, then choose Software Update. A dialog will appear on your desktop. Click the Install button in the dialog to begin the installation. You will be instructed to restart your Mac to complete the process.
After you restart your Mac, the Mac App Store icon will appear in your Dock. Simply click the icon to launch the Mac App Store, then enter your Apple ID.