While couples are usually married by a member of the clergy or Justice of the Peace, they could also choose to have a friend or family member officiate at their wedding. This person simply needs to apply for a One Day Marriage Designation from the Governor's office.
According to Massachusetts General Laws Ch. 207, sec 39, the Governor can designate non-clergy individuals to solemnize a marriage, such as a friend or a family member.
The application and instructions can be found here. Applications should be submitted at least six weeks but not more than three months before the wedding.
For more information about marriage, please see Massachusetts Law about Marriage.