Bism Illah wa as salaamu alaykum.
Shariyf went to see an execution shortly before Ramadhaan this year. He took the older children (11 and 13 years old) with him. Here is a general account of the process from start to finish.
There is a large area, the equivalent of a sand football field, that is designated for executions in Madinah. It is close to Mandarin Supermarket, for those who know the area. Executions are done on Mondays. The area is prepared from early morning, 7:00 a.m. perhaps. Several vehicles carrying the police officers arrive to set up the site and guard it. Tape is used to cordon off the area and keep the spectators at the allowed distance.
By around 9:00 a.m. (this is not precise, but somewhere between 8:30 and 9:30 a.m. is the time slot), the vehicle arrives with the person to be executed. Shortly afterwards arrives the special car bringing the executioner*. He is greeted by various officials and people. Then there is an announcement of what crime the person committed and the family members of the victim (or the victim, if they are alive) are asked if they have changed their mind and want to take the blood money from the criminal for their crime or if they want him to be executed. In this case, they wanted him to be executed. Then the executioner speaks to the person waiting to be executed. Although we cannot ascertain what he says, it seems apparent that he is telling him to make whatever dua' he wishes, prior to his execution. The executioner then checks with the criminal to see if he is finished. The execution is both swift and professional. The Executioner makes one clear swipe with his sword and turns away in one smooth movement as the head is falling to the ground.The executioner gives his salaams to the various officials and returns to the waiting car to be driven away.
My friend reported that there was an execution a few weeks ago of a young Saudi, who broke into a house and killed the woman when she tried to defend herself. The family of the woman were present and were asked prior to his execution if they wanted to forgive him and take blood money (dhiya) instead of the ordained punishment, but they opted for his death. On this occasion, the head didn't severe completely and he had to make another swipe.
There is a certain feeling of "living" Islam when these executions take place. In a world where Islam is cut to fit into lives rather than lives cut to fit Islam, it is reassuring to see the enforcement of Allah's commands for such grave crimes.
*You can find an interview done by Arab News with English subtitles on you tube, if you want to meet Saudi Arabia's executioner and hear what he has to say.