How to use a function pointer in a C struct?

I want to learn more about using function pointers in C structs as a way to emulate objects-oriented programming, but in my search, I've just found questions like this where the answer is simply to use a function pointer without describing how that would work.

My best guess is something like this

#include <stdio.h>
#include <stdlib.h>

struct my_struct
{
    int data;
    struct my_struct* (*set_data) (int);
};

struct my_struct* my_struct_set_data(struct my_struct* m, int new_data)
{
    m->data = new_data;
    return m;
}

struct my_struct* my_struct_create() {
    struct my_struct* result = malloc((sizeof(struct my_struct)));
    result->data = 0;
    result->set_data = my_struct_set_data;
    return result;
}

int main(int argc, const char* argv[])
{
    struct my_struct* thing = my_struct_create();
    thing->set_data(1);
    printf("%d\n", thing->data);
    free(thing);
    return 0;
}

But that give me compiler warnings warning: assignment from incompatible pointer type, so obviously I'm doing something wrong. Could someone please provide a small but complete example of how to use a function pointer in a C struct correctly?

My class taught in C does not even mention these. It makes me wonder whether these are actually used by C programmers. What are the advantages and disadvantages of using function pointers in C structs?