First, let's define situational irony. According to literarydevices.net,
"Situational irony is a literary device that you can easily identify in literary works. Simply, it occurs when incongruity appears between expectations of something to happen, and what actually happens instead."
In other words, situational irony is when the opposite of what the reader expects to happen in fact happens.
1) The very first sentence of the story sets the reader up with expectations of a story about a pleasant day and a pleasant gathering in a village:
"The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green."
Everything in the sentence, all of the imagery and descriptions, gives the reader a sense of joy and happiness and growth. But this is not the story that is told.
2) The reader doesn't know what "the lottery" is, but the assumption or expectation is that it's a normal, joyful town event. Jackson writes,
"The lottery was conducted--as were the square dances, the teen club, the Halloween program--by Mr. Summers. who had time and energy to devote to civic activities."
So "the lottery" is being compared to other events that most readers will have experienced. But again, the reader will discover later that the lottery is nothing at all like such events.
3) Right before the lottery is about to begin, Jackson describes the following:
"Mrs. Hutchinson craned her neck to see through the crowd and found her husband and children standing near the front. She tapped Mrs. Delacroix on the arm as a farewell and began to make her way through the crowd. The people separated good-humoredly to let her through: two or three people said. in voices just loud enough to be heard across the crowd, "Here comes your, Missus, Hutchinson," and "Bill, she made it after all." Mrs. Hutchinson reached her husband, and Mr. Summers, who had been waiting, said cheerfully. "Thought we were going to have to get on without you, Tessie." Mrs. Hutchinson said. grinning, "Wouldn't have me leave m'dishes in the sink, now, would you. Joe?," and soft laughter ran through the crowd as the people stirred back into position after Mrs. Hutchinson's arrival."
The words bolded in this paragraph, as well as the general casual and friendly tone, all set the reader up to believe that something pleasant or amusing is about to happen.
These are just three examples of situational irony. The reader awaits something good, when in fact at the end the reader learns that "the lottery" is a ritual wherein through a drawing, one of the village members is stoned to death by the rest of the villagers. Thus the complete opposite of what the reader expects, through the tone and language of the author, is what happens, which is situational irony.