Laws vary by state, but I can tell you, for sure, in Missouri you are a legal resident if you possess a valid Driver's License and/or Voter's Registration card.  There is probably a time element too, but I don't know what that is.  I checked into this for the purpose of attempting to purchase resident hunting licenses, as I own property there.  No way to do it, as my job requires a state license in Illinois.  It is virtually impossible to maintain a "dual residency," at least in these two states.  Drunk truck drivers screwed that up by having multiple driver's licenses in many states in years past.  Here's to 'em:  [-!-]

Whatever passes for a DMV--Department of Motor Vehicles, to get a new Driver's License.  Also, register to vote there--this year's election is very important to all of us.  

Note: you can only have one valid driver's license at a time.  If you get a license in another state, you'd have to either surrender your old license or have it hole-punched, rendering it legally invalid.

You *can* get a state ID card that looks similar to a driver's license, though, which is what most people do.  However, you'd need to own property in the new state, and may be required to prove it (utility bills in your name at that address, etc.), and you must live at that property at least part of the time.

Each state sets its own standards for what constitutes residency, so you have to figure that out for the state in question.

-Troy