Reinstalling OS in a 12 years old iMac

My employer gave me her old Mac desktop, 27 inch. she had it wiped clean. I am trying to reinstall operating system. I have watched videos and read a lot of articles but nothing works. It is 12 years old so I am not sure it is worth taking to apple and paying them to try to fix. If anyone can help I would appreciate it very much.

[Re-Titled by Moderator]