There are two approaches: shmget and mmap. I'll talk about mmap, since it's more modern and flexible, but you can take a look at man shmget (or this tutorial) if you'd rather use the old-style tools.
The mmap() function can be used to allocate memory buffers with highly customizable parameters to control access and permissions, and to back them with file-system storage if necessary.
The following function creates an in-memory buffer that a process can share with its children:
#include <stdio.h>
#include <stdlib.h>
#include <sys/mman.h>
void* create_shared_memory(size_t size) {
  // Our memory buffer will be readable and writable:
  int protection = PROT_READ | PROT_WRITE;
  // The buffer will be shared (meaning other processes can access it), but
  // anonymous (meaning third-party processes cannot obtain an address for it),
  // so only this process and its children will be able to use it:
  int visibility = MAP_SHARED | MAP_ANONYMOUS;
  // The remaining parameters to `mmap()` are not important for this use case,
  // but the manpage for `mmap` explains their purpose.
  return mmap(NULL, size, protection, visibility, -1, 0);
}
The following is an example program that uses the function defined above to allocate a buffer. The parent process will write a message, fork, and then wait for its child to modify the buffer. Both processes can read and write the shared memory.
#include <string.h>
#include <unistd.h>
int main() {
  char parent_message[] = "hello";  // parent process will write this message
  char child_message[] = "goodbye"; // child process will then write this one
  void* shmem = create_shared_memory(128);
  memcpy(shmem, parent_message, sizeof(parent_message));
  int pid = fork();
  if (pid == 0) {
    printf("Child read: %s\n", shmem);
    memcpy(shmem, child_message, sizeof(child_message));
    printf("Child wrote: %s\n", shmem);
  } else {
    printf("Parent read: %s\n", shmem);
    sleep(1);
    printf("After 1s, parent read: %s\n", shmem);
  }
}