This will take several phone calls and may seem hard but you have to do this right.
Typically changing services are free if you are moving locations and keeping the same provider. If you are going to have to purchase services from a new company because your current provider does not have services in your new area there may be a deposit for things like power and water.
Be sure to give the utilities specific dates about your move, you don't want to end up staying in a hotel at your new home because your waiting on them. If your moving plans change after you make the appointments be sure to let them know so they can update their records and take care of you. This goes for phone, internet, cable TV, water and gas!
Make sure to leave a forwarding address for your current providers so you can pay the last term of your service off, or better yet, you may have a deposit returned to you. Besides, you don't want hassles later on if you failed to pay a utility bill and they turn you over to collections.