I don't really recommend the "easiest" way to root and unlock because if something goes wrong, you may not know how to fix it. I recommend using SBenson's root and unlock guide in the Galaxy Nexus Development section. Only difference is instead of using the superboot.bat within the superboot zip, you just need to flash supersu through a custom recovery or flash a ROM.
http://download.chainfire.eu/212/SuperSU/CWM-SuperSU-v0.96.zip <---------------- SuperSU. Download and put it on your internal SD card.
Flashing a custom recovery is easy though. Just download a recovery img (either CWM, CWM touch, or TWRP) just make sure you download the toro version. Once you have that downloaded you'll need to put it in your fastboot directory (you created this when following SBenson's guide). Turn your phone off and then turn your phone on again holding volume +, volume - and power and connect it to your computer. In a terminal type:
cd location/of/fastboot/directory (if you followed SBenson's guide, it should be C:/root; so you would type: cd C:/root )
fastboot flash recovery NameOfRecovery.img
Then you would boot into recovery by navigating to where it says "RECOVERY" using the volume buttons. Click power once you see "RECOVERY". You should now be in your recovery of choice. You can either flash the superSU zip I gave you OR you can simply flash a rooted ROM. I'm partial to Slim JB, but if you want to remain fairly stock, Bugless Beast is a good way to go.