I first changed my mailing address to SD and did that over the phone with Alternative Resources in Sioux Falls. That gave me time to make sure all the important snail mail address changes were made. I rented a post office box where I was living at the time and had AR forward my mail to the box. I guess I could have used general delivery but didn't think of it at the time.
About 3 months later I made the trip to SD and got my driver's license, voter registration, vehicles registered, and insurance for my vehicles. I had to change insurance companies because my, then current, insurance company didn't do business in SD. Once that was done I was a SD resident and 2 months later moved out of the house and put it on the market.
Since I owned my motor home before I started all of this I didn't get the opportunity to save on sales tax but had I been able to it would have been worth about 3% of the price of the motor home. I was able to stop paying state and local income taxes for the latter half of the year and that was pretty nice.