One who commits a capital crime accidentally, and the act also incurred liability for payment, and we normally give only the greater of two punishments: Ketuvot 34b-35a
We may not accept payment in lieu of execution: Ketuvot 37b-38a
Procedure
The Court fasts on the day on which it administers capital punishment: Moed Katan 14b
The frequency of administration of the death penalty, in order for a court to be considered "bloodthirsty": Makkot 7a
How far judges would go to avoid administering capital punishment: Makkot 7a
Other Issues
Gd making sure a person suffers the equivalent of a death penalty he would have suffered at the hands of a court, were the court able to administer it: Ketuvot 30a-b; Sotah 8b