The most beautiful irony in the story comes through the imagery. The American and Jig are discussing an abortion. When Jig gets up from the table to look out over the landscape, all she sees are images of fertility: green trees, a flowing river, fields of grain. However, she turns from this image to return to the man, having lost the will to fight for her unborn child. Here is the fertile passage:
The girl stood up and walked to the end of the station. Across, on the other side, were fields of grain and trees along the banks of the Ebro. Far away, beyond the river, were mountains. The shadow of a cloud moved across the field of grain and she saw the river through the trees.
The other irony comes in the man's argument with the woman. He spends his time telling her how simple it will be and how it is the best thing - he clearly wants her to have the abortion. However, as soon as she says that she'll do it for him, he backs up, saying he doesn't really care, he just wants what is best:
'You've got to realize,' he said, ' that I don't want you to do it if you don't want to. I'm perfectly willing to go through with it if it means anything to you.'
He clearly wants her to decide to have the abortion, but doesn't want to be seen as having made the decision himself.
With irony being a contrast between what a character thinks and what the reader or audience know to be true, the reader must seek the difference between what the characters think and what he/she discerns about them.
Since the girl mentions the hills being like white elephants, she understands their meaning: She tells the man who says he has never seen a white elephant, "No, you wouldn't have." She is the one who expresses doubt about having an abortion. But the young man, who tries to convince the girl to have the operation, says that everything will be all right and the couple can return to their life beforehand. (He "buys" the white elephant, something one thinks has value, but does not.)
The irony of the title, then, is that the man "buys" a white elephant believing that the action under consideration can return him and his girlfriend to their former relationship, but the girl, like the reader, knows they will never be the same, for she turns from the vision of life, fields of grain and trees, and agrees to the man's putting their bags on the "other side of the station."
While there are other examples of irony in the story, my favorite example comes from the title. "The Hills Like White Elephants" should refer to the surrounding environment, and indeed it does. However, the girl is pregnant, and her belly will soon swell into a "hill." The infant is a classic "white elephant" for the man. As Wikipedia notes, a white elephant "is a valuable possession which its owner cannot dispose of and whose cost (particularly cost of upkeep) exceeds its usefulness." That baby is valuable, and the man is trying to get rid of it; it would cost too much (in terms of change, commitment, etc.) to keep it.