Assassination
On August 31, 1901, Czolgosz would travel to Buffalo, NY and stay at Walter Nowak's (novak) hotel, a fellow Pole that he knew from his time in Cleveland, where he would be safe from discrimination.1
It is important to mention the discrimination that Polish, Irish, etc. immigrants at the time went through, dealing with this for years was likely a factor that drove Czolgosz over the edge. A source from the time states that "we must remember that this man was an ignorant Pole, who spoke his own language most of the time" when talking about Czolgosz and goes on to say that "it would be quite impossible" for him to understand the previous presidential assassin, Charles Guiteau before going on to further paint them in a good light (presumably since he was labeled as a true American man).2
After checking in at the hotel, he would ask Nowak about the Presidents visit to the city and where he would be going. Nowak gave him all the info he needed, completely oblivious to Czolgosz's plans, so then he would head out and scope out the place where the event featuring the president would be for several days, visiting again and again. He would finally make up his mind on what he was going to do and went and bought a gun.3
After the President eventually arrived to the event, He would then spend the next three days stalking the president, resisting the urge to lunge, getting pushed aside by security and waiting for the perfect moment that would eventually come when Mckinley was greeting guests.4 Czolgosz waited for his turn, stuck out his left hand for a handshake, slapped aside the presidents, then lifted his right hand which had a hankerchief wrapped gun, and fired two times into the Presidents chest before being struck down and beaten by the crowd. Just after being shot, Mckinley suprisingly seemed in good health, saying to "go easy on him" before security took him away. He would later pass away eight days later due to the would getting infected.5
Footnotes
1. “Czolgosz Says He Had No Aid.” Chicago Sunday Tribune (8 Sept. 1901) v60n251: part 1, pp. 1, 4. http://mckinleydeath.com/documents/newspapers/CST60-251b.htm
2. Dr. Walter Channing. The mental Status of Czolgosz (Brookline, Mass: American Journal of Insanity, Vol. LIX, No. 2, 1902) pp. 40 https://archive.org/details/mentalstatusczo01changoog/page/n7/mode/2up
3. Everett, Marshall. n.d. "Complete Life of William McKinley and Story of His Assassination" 1901: pp. 66 https://archive.org/details/completelifewil01evergoog/page/n75/mode/2up
4. Everett, Marshall. n.d. "Complete Life of William McKinley and Story of His Assassination" pp. 69-70
5. “September 6, 1901 - Theodore Roosevelt Inaugural National Historic Site (U.S. National Park Service),” n.d. https://www.nps.gov/thri/september6.htm.