O'Connor establishes the foundation of the irony very early in the story when she gives us the reason for the grandmother getting dressed up for the car ride:
In case of an accident anyone seeing the dead on the highway would know at once that she was a lady.
At several points in the story, the grandmother judges people as good or bad based on her very quick assessment of how they look and behave. For example, the first time we see the phrase "A good man is hard to find," the speaker is Red Sam at the roadside barbecue restaurant where the family is having lunch. Just before that, however, Red Sam has described his willingness to allow some strangers to charge gas, and he asks himself the question, "Now, why did I do that?" The grandmother's immediate response is "Because you're a good man." She makes this assessment on the the barest of information about Red Sam, not on the basis of any meaningful knowledge about his character.
After the car crash and the Misfit and his cohorts make their appearance, and the grandmother recognizes the Misfit, his politeness, which is genuine but also calculated to put the family at ease, draws out the grandmother's assessment of the Misfit:
"Listen," the grandmother almost screamed, "I know you're a good man. You don't look a bit like you have common blood. I know you must come from nice people!"
Although it's quite possible that, in her desperation, she is trying to curry favor with the Misfit, the observation is also consistent with her judgment of people based on their physical appearance and outward behavior.
The great irony at this point is that the grandmother has completely mis-read the nature of the Misfit who, as we learn a short while later, is an absolute sociopath with a dash of the psychopath thrown in to the mix.
Another ironic twist occurs at the end of the story when, after talking to the Misfit about salvation and finally understanding how troubled and confused he is, the grandmother, who has been relentlessly superficial up to this point, has an epiphany and actually feels sympathy for the Misfit:
She saw the man's face twisted close to her own as if he were going to cry and she murmured, "Why you're one of my babies. You're one of my own children!" She reached out and touched him on the shoulder.
This act of compassion, however, is rewarded with three bullets to the chest. This is, perhaps, the greatest irony in the story: just when the grandmother becomes truly compassionate, finally moving past her self-absorption, she signs her own death warrant because the Misfit is not interested in compassion and understanding--his goal is survival, and the grandmother is a threat to that survival.