Resolved: A just society ought not use the death penalty as a form of punishment.First, "a just society." This phrase gives the Affirmative a task and a burden to levy on the Neg. The task: defining justice in a societal framework. More to the point, the harms of the death penalty must be harms against society, or harms incurred through societal mechanisms. If the death penalty, for example, is racially unbalanced in application, the Aff can't just say "the death penalty is racist." The Aff must show why this is opposite the values of a just society--and the word "ought" will become important here, too, since it establishes the criterion for a just society. Is it an ought of utility? An ought of constitutionalism? An ought of democracy?
Secondly, the Aff must remember to place a specific burden: whatever goods the Neg claims about the death penalty, they must be linked to justice in a societal framework. The Aff can't allow the Neg to say "but the death penalty is an effective deterrent!" without concurrently showing why deterrence is a valid and sufficient aim of punishment in a just society. This goes double for any arguments based on individual liberties, no matter which side proffers them. What is the connection between individual liberty and a just society? It must be made explicit.
The overarching point is that all arguments must link back to a vision of the just society, and any argument that strays beyond can be dismissed as nonresolutional (or, to sound a little less debaterish, irrelevant).
I haven't worked out in my own mind exactly how "as a form of punishment" affects either side of the resolution, other than to note that punishment's effects go beyond the punished. Punishment can be retributive, torturous, instructive, deterrent, preventive, excessive, slight, fitting, cruel, unusual. It can be examined empirically and philosophically. The ultimate question in the background, as alluded to before, is, "What is the role of punishment in a just society?" This essay might point you toward some initial answers.