First if you are seeing the Mac drive and the recovery partition you are in the wrong place. Boot the Mac normally (without holding option) and get to the desktop screen of the mac.
Buy a USB to Sata cable. Or a Sata drive dock with USB connector. Connect the hard drive. Turn it on then plug in the USB cable to the Mac. You should then be able to copy the readable files on the drive to the Mac.
Note that I said "readable" files. You will not be able to copy any files that would not be useable on the mac. An example would be Microsoft Word Files. Once you copy them to the Mac you can launch MS Word and from the Open menu navigate to the files and open them as needed. You may need to switch the pop-up menu in the Open dialog to "View...