John 19: 16-22, To Golgotha

Jesus has been arrested and tried before Annas & Caiaphas, then before Pilate. Pilate, knowing that the Jewish leaders want Jesus crucified, attempts to placate the leaders but is threatened by the leaders' claim that Jesus wants to be king.

John 19: 16-20, Golgotha

Finally Pilate handed him over to them to be crucified.
So the soldiers took charge of Jesus. 
17 Carrying his own cross, he went out to the place of the Skull (which in Aramaic is called Golgotha). 
18 There they crucified him, and with him two others—one on each side and Jesus in the middle.

19 Pilate had a notice prepared and fastened to the cross. It read: jesus of nazareth, the king of the jews. 
20 Many of the Jews read this sign, for the place where Jesus was crucified was near the city, and the sign was written in Aramaic, Latin and Greek. 

The crucifixion is described quickly simply. Jesus is crucified alongside a highway. Presumably this was common, to publicize what happens to those who disobey the Roman emperor and Roman law. The notice Pilate prepares shows his anger with the Jews. It effectively says, "This is what happens to your kings."

John 19: 21-22, What I have written...

The chief priests of the Jews protested to Pilate, “Do not write ‘The King of the Jews,’ but that this man claimed to be king of the Jews.”

22 Pilate answered, “What I have written, I have written.”

The leaders take offense to Pilate's summary and Pilate is in no mood to humor them. The religious leaders have claimed that they have no king but Caesar -- in contrast to their many claims before to be "free" -- and so they must put up with even Pilate seeing through their hypocrisy.