Q: I need to copy files from 1 hard drive to another.

I bought a new, faster hard drive (800 Mbps vs 400 Mbps), and I need to copy files from the old hard drive to my new one. I tried dragged them from old to new and got a ton of aliases that won’t work after the old hard drive is turned off and disconnected. I don't have any third party copy software. (I've never needed it on this computer.) This should be simple, but what I did failed. What did I do wrong? And what should I have done? (My OS is Yosemite, Version 10.10.5 and my computer is a Mac Pro.)