You contact Cricket and tell then that you want to port your number into a Cricket account. Whether you can use your S3 is another matter. Cricket WAS a CDMA carrier, but with AT&T buying them I don't know where they stand now. (Or whose network they're on if they're CDMA.)
As far as the port itself goes, once you do the paperwork with Cricket, they do the rest. DO NOT cancel your account with Verizon or you'll lose your number.