Probably the easiest is the Logan Express Bus to Framingham, $12 from the airport:
http://www.massport.com/logan-airpor...ss/framingham/ . Runs every 30 min on weekdays and every hour on weekends. The "Logan Express Bus" service is very well signed landside in the ground transportation area.
There are other options if you are adventurous; for example you can take the Silver Line bus service to South Station (free) then take the commuter rail to Framingham Station ($8.50) or similarly you could take the Back Bay Shuttle (free if you display a CharlieCard, $5 otherwise) and catch the same commuter rail line there; but this is much slower and the rail service is infrequent during many parts of the day.