Moving to another city, state or country means you have to take some time in getting the necessary stuff that will make your residency in that particular place legitimate. First thing would be to get all the needed things like drivers licenses, health cards and the like. Your car needs to be registered in your new address as well. There is a 90 day grace period though it must be noted that oging over the grace period will results into penalties and such.
If you want home delivery and such, remember to register in these things as well. If you are staying in that place for good or for a long period of time, then register to vote. Laws vary from state to state so it is best to contact a lawyer to ask about the particular laws as it will help you abide by these rules no matter how small or weird they may be.