What year is your MacBook Pro? Need to make sure you have the hardware spec for Mt. Lion. You should also consider 8GB of memory for reasonable performance.
Find how much storage: Apple Menu > About this Mac > More Info... > Storage
If you are within 80% of filling your current drive, you may have enough to install Mt. Lion, but the subsequent installation will not perform well due to storage saturation.
Before you update to Mountain Lion, you should do one last software update on Lion, then run Disk Utility and verify/repair permissions. Then back-up your home directory for safety, even though a Mt. Lion upgrade will not disturb your home directory.
If Mountain Lion actually did download, the installer is placed in your /Application folder as, Install OS X Mountain Lion. If you want a bootable USB Mountain Lion installer, now is the time to make it with Lion Diskmaker and a empty 8GB USB stick. After you run the Mountain Lion installer, it will de-install itself. Like Lion, you still have a bootable Recovery partition.