I am for the death penalty, especially if it is beyond a shadow of a doubt that someone did it. Although due process must be followed.
As for how to do it:
I say hangings are the way to go. Build a galloes right in the center of death row, and make sure the inmates have unrestricted view of it.
Cheapest way would be for the condemend inmate to go into the backyard cemetary beyond the prison, dig his own grave, then have the executioner have the condemend inmate stand over his grave, then shoot him in the base of the skull with a .22. Inmate falls into hole, and they bury his butt. Case closed.