For most Motorolas, you can just buy a cheap unlock code. There's plenty on Ebay for about £2, just pick one with decent feedback.
You will need the IMEI number for your phone, you can get that by dialling *#06#
Then put another network's SIM in the phone and switch it on, it will prompt for the unlock code.
I've unlocked a couple of Moto G / Moto E, worked fine. Only problem was changing the voicemail number, that seems to be locked to Tesco. But you can just save the correct voicemail in the contacts anyway.