10.6 (Snow Leopard), 10.7 (Lion), and 10.8 (Mountain Lion) are upgrades that you have to buy, they are not free updates for 10.5 (Leopard).
You would need to buy the Snow Leopard DVD and install it before you get the App Store application to buy either Lion or Mountain Lion. To get Lion, you would also need to call Apple to obtain authorization to download it, since it is no longer current.
You also need to verify that your MacBook Pro meets the specifications needed for these upgrades. You have provided no information about it. Click on the Apple Menu's, "About This Mac," to determine the version of you your MacBook Pro. You would need at least a MacBook Pro 3.1 to be able to use Mountain Lion.