So I want to root my moto x 2014 to try out this whole cyanogen thing, however due to the plan that I am on at Verizon, I can turn in my phone in a few months to get a new one. I was wondering if I would be able to save my current phones state somewhere so that when I want to turn the phone in, I could apply the old settings so they would not know that it is rooted.
You can make backup of your android os and when you want to return your phone, you need to unroot it (if its locked) and then restore from backup
I figured that you could do it, what I need to know is how to do that.
you need some kind of custom recovery (CWM, TWRP e.c). When you have installed that then you need to boot into recovery (If OS supports straight from there or via button combination). There will be backup option.
You can also use Titanium Backup
I do not think you can unlock your boot loader on the Verizon version of the moto x. To unlock a normal moto x you would use Motorola's website to get a unlock code but Verizon hates flashing roms so they usually block that. You can check here if its eligible.