The first thing necessary here is to understand the terms judicial activism and judicial restraint. Judicial restraint refers to rulings from the Court that take a view of interpreting law and applying law rather than making law. Judicial activists are those judges who believe their job is to legislate from the bench - to make law. Judges who practice judicial restraint believe that legislating -making law- is for the Congress (or other legislative body) and not for the Judicial Branch. Our current Chief Justice of the Supreme Court, John Roberts, explained this during his confirmation hearing in the Senate when he was asked if he believed in judicial activism or judicial restraint. He said: I consider myself to be an umpire; I'm not batting and I'm not pitching; I'm just calling the balls and strikes. Clearly, the Chief Justice believes in judicial restraint.
Your question -about a particular ruling- should be easier for you to answer once you understand the difference. In the Citizens United case you are looking at, the Court determined that the law restricting campaign donations was a violation of the First Amendment right to freedom of speech. The Court was interpreting and applying the First Amendment of the Constitution to the campaign finance law.
Look back over the NY Times article with this information in mind, and you should be able to complete your assignment.