What if the person is Muslim? Or Buddhist? or Hindu? How do you do that?
It’s a mistake to attempt to fight irrationality with rationality. I highly recommend contempt, though.
In the same way, by being careful not to insult their religious sensibilities.
However, I have never heard of any Buddhist or Hindu having religious objections to evolution, and the rather few Muslims that do seem to have picked up the idea from the fundamentalist Christians. It is not part of traditional Islam (we had a GQ thread about this recently). The insistence on taking your creation myth ultra-literally is an aberration, a 20th century American aberration, in Christianity, and not one that has any real equivalent in other religious traditions.
Anyway, the American fundamentalist anti-evolutionists are not against evolution because they think it contradicts the Bible, they are against evolution because they hate the ways society is changing, and they think that if evolution is true it implies that that social change is inevitable and is to be welcomed as progress. They are, first and foremost, social reactionaries, who turn to a literalist reading of the Bible as a weapon to fight the ideology of social change and progress. Those people are unreachable anyway, and it is pointless to argue with them, but they are a fairly small minority and would have little influence if others did not buy into their highly skewed, simplistic and ahistorical account of what it is to be Christian.
The people I was talking about in my post above, the majority of those who say they reject evolution, are simply the ones who have ignorantly fallen for the conservative fundamentalist propaganda that tells them (falsely) that true Christians must take everything in the Bible literally, and that you can’t be both a Christian and an evolutionist. The trouble is that far to many of the would-be defenders of evolution have fallen for this propaganda too, fail to distinguish between fanatical reactionary “Christians” and traditional and moderate ones who are simply ignorant about the traditional Christian doctrine about the relationship between religion and science (i.e., St Augustine’s teaching that Christians should not fight science, and that where there is a conflict between science and one’s interpretation of the Bible, it is the Bible interpretation that must give way). Those evolutionists and militant atheists who have bought into the fundamentalist propaganda about what Christianity is are helping to drive the more moderate and potentially open-minded majority of American Christians (most of whom care far more about their emotional attachment to their religion than about some dry scientific theory) into the arms of the fundamentalist-reactionary fanatics.
Most of the people who say they do not accept evolution are not irrational, they are just ignorant, and the more important aspect of their ignorance is not what they do not know about about science, but what they do not know about the religion they are attached to.
If you give up on them, and drive them into the arms of the real irrational fanatics by showing your contempt, you have lost the game, and the new dark ages are on their way. (Of course, they may be on their way regardless. :()
Fight ignorance? Pshaw! Why would we want to do that? Contempt is more emotionally satisfying.
Uh … yeah, right. Openly showing contempt for them is always a great way to get them to listen to you with an open mind. And it doesn’t make you look malicious or conceited or anything. Everybody watching will be greatly impressed with your snarling and spitting.
And we wonder why it’s taking longer than we thought.
I’ve come across a lot of people who clearly are personally offended by the idea of evolution. The usual response is “I didn’t come from a monkey,” stated in a tone of resentment. Most of them weren’t fundamentalists or highly religious people, either.
Strange to say, but a lot of folks care very little about whether or not evolution is true. They’re busy with their personal lives, and the subject doesn’t interest them very much, so they don’t care to spend much time on it. “I didn’t come from a monkey,” is enough for them. At that point, the subject is closed so far as they’re concerned, and they turn their attention back to paying the rent and putting beans on the table.
And you know what? That’s perfectly okay. Just because you’re heavily invested in an issue doesn’t mean everybody else has to be.
They do if they’re teaching high school biology.
We don’t need to convince everyone on earth to accept the reality of evolution any more than we need to convince everyone that Maxwell’s equations work or that gravity is real. The important thing is to teach the scientific method then, using that method, show how we get from one piece of knowledge to another. My feeling is that evolution is too big of a subject for introductory students to grasp and should be left for college, thus ending the debate.
In high school science we should be using repeatable experiments to demonstrate the nature of our world. Once the creationists have a repeatable demonstration of a supernatural being creating life, then that should absolutely be included in the curriculum. It would be awesome and would prepare our children for further supernatural studies.
And if they’re teaching high school biology, they also need to understand that people who don’t share their belief in Darwinian evolution don’t necessarily deserve to be held in contempt. As my second year biology teacher in high school said, “I don’t require you to believe evolution, but I do require you to understand it.” He made it clear that only the conventional neo-Darwinian theory of evolution would be taught and discussed in class, and anyone who had religious or philosophical objections to neo-Darwinism would have to discuss those objectsion outside of class. He also gave a standing invitation to any student to discuss those objections with him after school. Several times small groups of students met with him after school to do exactly that. That’s the way to handle these things.
You’re asking what evidence will convince people who aren’t convinced by evidence. Obviously there is none.
Find a religious authority they listen to and have him tell them that evolution is real and doesn’t conflict with their religion. That may work. Or they may decide the religious authority has lost his faith.
That’s fine right up to the point where you try to convince them it’s a bad idea to overuse antibiotics. Because you need to understand and accept evolution in order to understand why antibiotic abuse is bad. And the people who reject evolution and abuse antibiotics will screw it up for everyone else.
Sometimes ignorance really can be dangerous. And not just to the ignorant.
The real question is not ‘how’ do we convince these people but ‘why.’
In the case of the biology teacher, they are free to believe whatever in the hell they want to. Just don’t teach it to your students. Period. You teach science and that means the science that is part of the curriculum. Don’t like it? Either suck it up or find another job.
In the case of other people, I suspect that eventually these people will die off and the percentage of people who believe in the literal creation myth will reduce.
For the most part, it is not possible to convert the unwashed masses or worth the effort.
Rejection of Evolutionary theory isn’t a logical matter so approaching it with logic isn’t going to fix the situation. That’s really the crux of the problem though and why it’s such a controversial issue because supporters of evolutionary theory support it for logical reasons and attempt to convince their opponents with logic whereas those who reject it do so for emotional or intuitive reasons and try to convince their opponents for the same reason.
To give an example, it would be like trying to convince a fan of a specific sports team that another team is better because they’ve won more championships or have a better win ratio or whatever. The fan will appeal to how they came to love the team they love, how much more entertaining they are, specific moments that are memorable, or why a specific championship is somehow more meaningful than other ones.
Now, of course, it can easily lead to misunderstanding in both perspectives because if one doesn’t really want to put in the effort to believe or understand something, they’re not going to. So those who deny it will often not really understand a lot of the mechanisms. Similarly, those who support it don’t understand how to argue the aspects of evolutionary theory that aren’t intuitive or easily understood.
And as far as teaching goes, for a science class, teaching anything other than well accepted scientific theory doesn’t make sense outside of the context of discussing currently developing research and trying to explain the difference between the various ideas. It does make sense to discuss controversy too, since controversy isn’t limited just to evolution nor to the sciences, but it’s important to keep the context of the controversy and that something is controversial does not mean anything specific about the validity of the arguments of both sides. Afterall, this controversy is enough of the zeitgeist that they’re bound to run into it when studying it, not so much for modern flat-Earthers or whatever.
No, that’s not what the OP is asking. Read it again. The OP is asking how to change people’s intuition.
I see this often in mathematics, where something is counterintuitive or “paradoxical” (like the “birthday paradox” or the infamous “Monty Hall problem”). You can give a formal proof, with correct equations and impeccable logic; or you can give an intuitive argument that tries to change people’s intuition, to give people a feel for why something’s true. Both have their place. Both have their place.
The first thing I would do (and to to creationists who wander into GD) is to ask them to explain what evolution is. A lot of them have been told by their preachers that evolution says all sorts of ridiculous things, like dogs turn into cats. Their intuition - and logic - tells them that this definition of evolution is absurd, and since you can agree with them, that might help.
Then you can explain descent with modification. That is a fairly simple concept. Natural selection is even simpler.
Some people have creationism so linked to god which is so linked to their reason for living that you won’t be able to break it. But slightly more rational people might be open to thinking about what science really says.
As for religion, believing in religion does not imply being a creationist, but being a creationist implies believing in religion.
“Prove it.”
This all sounds like a lot of work; I’m going to stick with “Shovel to the back of the head.” 
No, you don’t.
Someone always brings this up as some big “gotcha” for Creationists. It’s not.
Creationists know you can manipulate genes. They don’t refute that dog breeds were created. And a drug-resistant bacterium is no different from a non-shedding dog. There is no reason that Creationists can’t accept what they call “micro-evolution”. Things can change a little bit, but dogs can’t turn into cats and monkeys can’t turn into humans.
Hmmm … it would take an awful lot to convince me that there is some substantial link between misuse of antibiotics and rejection of evolution.