So, my hard drive is slowly dying . . . about all I'm able to access is the recovery partition. I bought a new hard drive to replace it, but no longer have the install disks that came with the computer. How do I make install disks from the recovery partition that I can use to install Mountain Lion back onto the new hard drive?
If you have a Mid 2010 MacBook Pro or newer, you have Internet Recovery, so you can reinstall OS X pressing Command, Option and R keys while your Mac is starting, without needing to have OS X on the hard disk
You have two possibilities:
1. Open App Store > Purchases and download Mountain Lion. When the download has finished, open Lion Diskmaker to make a bootable Mountain Lion USB drive > http://blog.gete.net/lion-diskmaker-us/
2. Download Recovery Disk Assistant from the Support website to create a Recovery HD on your USB drive.
The difference between them is that the first contains OS X Mountain Lion, so you won't have to download Mountain Lion from the App Store when you are going to install Mountain Lion
mende1 is referring to OS X (Lion/Mountain Lion)- About OS X Recovery. See also, Computers that can be upgraded to use OS X Internet Recovery to determine if your particular model is able to use Internet Recovery.