Citizens, or residents, of Montana enjoy certain privileges over non-citizens (or residents from other states). For instance, fishing and hunting license fees are cheaper and Montana residents enjoy lower tuition fees for colleges and universities within the state. Establishing residency is a matter of proving to the state you intend to remain in the state permanently. After becoming domiciled for a certain number of days, Montana considers you a resident of that state.
Rent or purchase a home or apartment. If renting, sign a 12-month lease at a minimum.
Get employed. While not specifically required, employment shows you intend to remain in an area for a long period of time.
Obtain a driver's license. Apply for a Montana driver's license at a local secretary of state office. You are eligible for a Montana license after living in Montana for 60 consecutive days.
Live and work in Montana for at least 180 days. After getting a job and a Montana driver's license, all you need to do is live and work in Montana. After 180 days you are considered a resident (according to Mt.gov). Note that for education purposes (such as to attend college) you must live in Montana for one full year.
Live in Montana at least 120 days out of each consecutive year to keep your residency status.