How are death sentences passed?

Answer 1

India:

Hanging is the method of execution in the civilian court system, according to the Indian Criminal Procedure Code. Under the 1950 Army Act, hanging as well as shooting are both listed as official methods of execution in the military court-martial system.

Answer 2

That depends on what court in what country. Here in the US, it is a part of the judgement of the court, read aloud by the clerk of the court or judge, and published. It will usually contain the phrase that the condemned person has been found guilty of a capital crime, and is "to be taken to a place of execution, and put to death in a manner proscribed by law." Below is an actual sentence from Florida in 2001:

ORDERED AND ADJUDGED that the defendant, JOHN DOE, is hereby sentenced to death for the murder of the victim, DOROTHY JONES. The defendant is hereby committed to the custody of the Department of Corrections of the State of Florida for execution of this sentence as provided by law.