Thanks to the Kexec boot process developed by "CVPCS" for the Verizon Galaxy S III we are able to now install custom Roms like CM10 and AOKP to our devices. The Kexec boot process basically circumvents the locked bootloader allowing us to do pretty much anything that we want to our phones! All this techy talk can be intimidating to someone who is new to rooting. That's why Guides and Tutorials are so important in this community. "SqueakyBigFoot" has put together a super easy CM10 install guide for the Verizon Galaxy S III. Literally just follow the 6 step guide to install CM9 or CM10 to your new phone. It is very easy and takes only about 5 minutes.
The Guide plus download links can be found here.