What is required to get your child in a new school, new city.

It really would depend on the school district.  Most school districts will require some proof of identification and then proof of residency.  (Birth certificates, phone/electricity bill or driver's license with new address in parent's names.)

I would call the elementary school your kids will be going to, and ask them for their specific requirements.  Usually they'll want to set up an appointment for you to come in and register your children prior to the beginning of the school year.