Hi tfaranyosi,
Thanks for reaching out to the Apple Support Communities. I understand you need to know how to install the OS X Mountain Lion operating system on the blank hard drive hat you have installed in your 2009 MacBook. The current documents that are available online show how to do so from El Capitan to the current macOS Catalina.
Since you have purchased the installer already, be sure to first make a copy of the file in the event you need to work through these steps again. Next, you should be able to use your MacBook Air and follow these steps to create a bootable USB installer:
- Right-click or Control click on “Install Mac OS X Mountain Lion.app” and from the menu that pops up, select “Show Package Contents”
- Open the “Contents” directory and then open “SharedSupport”, looking for a file named “InstallESD.dmg”
- Double-click on InstallESD.dmg to mount it on the desktop
- Launch Disk Utility (you'll find this in a folder called Utilities inside the Applications folder) and connect a USB drive to the Mac. This can be either a traditional external drive or a good-sized flash drive.
- Select the USB drive from the left menu and click on “Erase” tab, choose “Mac OS X Extended (Journaled)” as the format, then click on the “Erase” button in the corner
- Now select the formatted USB drive from the left side and click on the “Restore” tab
- Drag the previously mounted “Mac OS X Install ESD” image into the “Source” section
- Drag the formatted partition to the “Destination” section, then click on “Restore”
- Confirm that the USB drive will be erased and enter the Admin password for the Mac when asked
Disk Utility will now create a bootable OS X Mountain Lion installer drive out of USB drive using the disk image, this can take a little while depending on how fast the drive and Mac are but 20-30 minutes isn’t unusual.
When finished, connect the USB drive to the Mac you are trying to install Mountain Lion on and hold down the Option key while booting up to bring up the boot menu.
Select the orange “Mac OS X” option and you will boot into the OS X Mountain Lion installer, from here installation is the same as normal. Click on Continue, select the destination drive, and install.
Let me know how this works.
Cheers.