Try posting on our off-campus facebook group; possibly a current off-campus student has an available room. Many Hampshire students have luck finding an apartment on Craigslist, which is very active in western Massachusetts. We have also compiled a list of local rental agencies for your convenience.
There is an entire section of the University of Massachusetts website devoted to off-campus services, which is full of useful information, including a listing of rentals and students looking for housemates.
New England Premiere (a local real estate agency) provides an Undergraduate Apartment Hunting Checklist, a useful guideline for those house-hunting for the first time.