NCLEX is a one-time thing, thank Goodness! Once you pass and are licensed in the state of your choice, you can obtain a new license in another state by endorsement. You apply to the new state, provide evidence of having a license in good standing in the original state, pay the licensure fee, and if desired, request a temporary permit to practice while your license is being processed. Obtaining licensure by endorsement can take a few months, so it is helpful to plan ahead if you are moving or traveling.
We've moved quite a bit with my Hubby's job. I'm the proud holder of 5 licenses, and have found a piece of advice from an instructor to be very helpful....Always keep your original license active. Even if you move and don't plan to return to that state, having an active license gives you a higher priority with that state's BON should you need information forwarded elsewhere to obtain a license by endorsement. That has been true for me. IL is the state of my original license, and I'm told that those with inactive IL licenses sometimes have to wait as long as 6 months for the IL Department of Professional Regulation to answer their requests for endorsement information. I've never had more than a few week's wait.
There are also some states, known as "compact" states which agree to accept each other's licensure. Not all states participate in this however, because of differences in continuing education requirements and other considerations.