Q: How do I update to Safari 6. I have Safari 4.0.3

I am not running OS X Lion. 

Why OS X Lion and not OS X Mountain Lion?

Thanks, I obviously have no idea what I'm doing

SHOULD I DOWNLOAD THIS?  I currently have this Mac OS X 10.5.8. 

About OS X Mountain Lion Update v10.8.3 (Combo)

The 10.8.3 update is recommended for all OS X Mountain Lion users and includes features and fixes that improve the stability, compatibility, and security of your Mac, including the following:

• The ability to redeem iTunes gift cards in the Mac App Store using your Mac's built-in camera
• Boot Camp support for installing Windows 8
• Boot Camp support for Macs with a 3TB hard drive
• A fix for an issue that could cause a file URL to quit apps unexpectedly
• A fix for an issue that may cause Logic Pro to become unresponsive when using certain plug-ins
• A fix for an issue that may cause audio to stutter on 2011 iMacs
• Includes Safari 6.0.3

For detailed information about this update, please visit: http://support.apple.com/kb/HT5612

For detailed information about the security content of this update, please visit:http://support.apple.com/kb/HT1222

SHA1 =1bc49fde5ff6e252aa7908b4cb1f9cb9c8a5fa29

I got to Step 2 and I'm stuck.... Do I need Snow Leopard?  

Thanks Niel.  I appreciate your help.