Introduce the topic by giving a brief explanation of how the judicial process for the death penalty works, then talk about what kind of people are accused and put on death row, and then talk about execution and exoneration.
Other good talking points: how so many inmates are severely mentally ill and are executed anyway despite it being unlawful to execute someone who is mentally incapacitated. Also mention how racism is a big factor in indictment, look at the numbers, you will find that the majority of the inmates are people of color, despite people who are not of color killing people too. And finally, it would be good to talk about the lethal injection process and how many find it to be cruel and unusual punishment as it is questionable whether after the first injection (which is a light anesthetic) if the inmate is truly asleep. The second shot is often administered without knowing whether the inmate is fully under the anesthetic, and as it paralyzes all the voluntary muscles (something that is incredibly painful) many inmates are still awake and must suffer through this process. Another thing is that without the death penalty, taxes would be lower, because the state would not need to fund public defenders and investigators to work on the cases of those not capable of affording a private lawyer (the vast majority of inmates) and the inmates would just get life without possibility of parole.