According to the Secretary of State's office - citizen information service, there is no formal procedure for establishing a legal residence in Massachusetts. Normally tangible proof of residency is provided through:
Appearance of a person's name on a city or town street list
Rent / mortgage receipt
Utility or telephone bills
Individual public or private agencies or institutions may have their own requirements for proof of residency.
The Secretary of State's Office has a brochure titled "Welcome to Massachusetts, a Practical Guide about Living in the State." The state's website is useful as well.
State Tuition Rate Qualification
A 1-year residency requirement is imposed in order to qualify for state tuition rates at state colleges and universities, and a 6-month residency is required for the community colleges.
If you are a U.S. Citizen, a Massachusetts resident, and you will be 18 years old on or before election day, you may register to vote at any city or town hall in person, or by registering online here.
For more information about voting please see the voter registration page.