Here is Spiridovitch's first hand account, from"Les Dernieres Annees.." Vol. 2 Ch. 4. The translation from the French is mine, (copyright Rob Moshein 2005):
When I went to the theater on the day of the performance, I found all of my men at their posts. The control posts were already in place. My adjutant, Lt.Col. Oupravine, who was directing the service, reported that the inspection of the theater had been made, and all of my orders were followed to the letter.
The curtain rose. I was in such a state that that I understood absolutely nothing which was happening on stage; each instant I thought I heard steps in the aisle and, despite myself, I would turn around, obsessed by indescribable anxiety.
At the end of the first act, when the Emperor left his box, I went into the corridor to make sure that the guard supposed to be posted there during the intermission was actually in place, in front of the Emperor's entrance. I saw neither Kourlov nor Koubliako in the corridor. I saw only Vyerigine, some ways off, busy as always, approaching everyone with a mysterious, conspiritorial air.
Here is what I know on my part. After the second act, the Emperor left his box to take tea in an adjacent room. His children followed. The Imperial box was empty. I went again out into the corridor. No one was left on the parterre. Stolypin was standing in front of the ramp separating the parterre from the orchestra, his back to the stage. On his right were Baron Freedericks and Gen. Souhkomlinov. Yessaoulov had gone to smoke.
Along the aisle to the left, a young man in elegant clothes calmly approached the group of those three men. Arriving at the top of the fourth row of seats, he fired three shots at Stolypin. Someone in the orchestra shouted. The Minister put his hand to his chest, and staggered.
"I am wounded" he said; then he took off, mechanically, his frock coat, dropped it on the ramp, look at the blood pouring out and fell without a sound into his seat.
"I am happy to die for the Tsar" the Minister said. He turned toward the Imperial Box, then seeing the Emperor who had entered the box, he made a gesture with both hands to tell the Emperor to go back.
The Minister was immediately surrounded by the people in the hall, to care for him, and they carried him off.
The young man, after firing the gunshots, went calmly still towards an exit. Suddenly he started to run. He was immediately caught, grabbed, thrown to the ground, and beaten.