There is not much known about the Roman “trial" of Jesus. The Romans took great pride in their system of justice, but the provisions of their law only applied to Roman citizens. It is known that the Romans allowed a great deal of freedom to non citizens in subject territories, but they retained tight control over those things that could affect their ability to govern. In particular, they retained control over capital punishment. The Jews tried to get Pilate to approve the result of their trial without specifying the charge. When this fell through they changed the charge from blasphemy to treason (an attempt to overthrow Caesar). It doesn't appear that Pilate conducted a full trial of Jesus. It was more like a preliminary examination to see if the charge had merit. Pilate twice announced that he found no merit to the charge. This should have ended the proceedings and Jesus should have been released. Pilate tried to hand Jesus over to Herod, when he found out that Jesus was from Galilee. Herod was intrigued by Jesus, but had no intention of taking responsibility for his trial. Pilate finally gave into the pressure from the Jewish crowd and handed Jesus over to be crucified.
It is not known exactly where the crucifixion took place, but it was outside the city. Usually the Romans placed the cross near a public road so that it could be seen by those passing by. The crosses were not usually as large as often pictured. The were generally only a foot or so larger than the height of the person. Sometimes they would use a tree to which they nailed the cross beam. The body was usually left on the cross for the animals to devour.