How long has it been since you bought a computer? Last one I bought didn't come with enough paper to have anything to root around in.
I got a new iMac a month ago. It had a pamphlet that tips the user to Migration Assistant, if needed, as well as explain what the various ports are.
I’m not an IT specialist, but I have done migrations from old to new macs many times.
If the OP had a backup drive of their old Zen, they should be able to hook it up to the new one and restore it there.
...Just as you suggest.