After rebooting mac, backup from hard drive was too large and didn't happen. I continued the reboot and can safely use my mac now, but how do I transfer the backup files I need from my hard drive onto my mac/macs system?

Seems like a silly question but I had an appointment at my local apple store about a start up issue, ran some tests and passed them which was fine.

After this, I was left to reboot my mac and basically transfer files from my harddrive onto my macbook. However, I couldn't choose the files to be transferred and so I went with the reboot and the startup issue I initially had was fixed, although I need the files from my hardrive to be transfered onto my mac.

There are backups and documents I need.