In the vice presidential debate on October 5, Cheney asserted that "in Massachusetts we had the Massachusetts Supreme Court direct the state of -- the legislature of Massachusetts to modify their constitution to allow gay marriage". One can evaluate the accuracy of his statement by looking at the November 2003 court decision Cheney refers to, Goodridge v. Department of Public Health.
In its decision, the court majority declared the prevention of same-sex marriages unconstitutional, altered the common law definition of marriage to include same-sex couples, and told the state that this modification would go into effect in 180 days (May 2004) in order "to permit the Legislature to take such action as it may deem appropriate." Amherst College Ney Professor of Jurisprudence Hadley Arkes -- hardly sympathetic to same-sex marriages --affirmed that the court "gave the legislature six months to alter the laws, or come up with some accommodation." Hence, the legislature wasn't ordered to do anything. It could have explicitly declared the right of gay couples to marry by attempting to amend the state's constitution, or by modifying the state's marriage licensing statute (which is a general law, not a section of the constitution). It could have also just sat back and done nothing.
The legislature instead acted in a way diametrically opposed to how Cheney (misleadingly) claimed it was directed. In December 2003 a bill was introduced granting gay couples the rights to civil unions but prohibiting them from marrying. At the Senate's request for clarification as to whether this bill was constitutional, the Supreme Court answered unequivocally, "no." The court also reiterated that the "purpose of the [180-day] stay was to afford the Legislature an opportunity to conform the existing statutes" to the court's earlier Goodridge decision (again, perhaps by modifying marriage licensing statutes).
Undeterred, the legislature moved to "modify their constitution" to disallow gay marriage, passing an amendment in March similarly prohibiting same-sex marriage but allowing civil unions. In order to actually change the constitution, the amendment requires a second vote next year and a popular referendum. Recent news indicates that this is becoming unlikely.