If the game you are trying to copy is not protected the copying process is the same. Sometimes it is harder to copy a copy. I have a couple of backups that can't be copied because the copy is harder to read in your pc. Stick to originals. Try using Clonecd or psxcopy v5. I found both these programs useful when starting out. But psxcopy caused a hardware conflict when I got a new motherboard.
Clonecd can also be used with patches
Cheers