The standard UNIX way is to use fork(2) followed by an exec(3) call (there's a whole family of them—choose whichever suits your needs the best).
Example to illustrate usage:
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
int main(int argc, char **argv)
{
pid_t pid;
printf("before fork\n");
if ((pid = fork()) < 0) {
//It may fail -- super rare
perror("Fork failed");
} else if (pid > 0) {
//If it returns a positive number, you're in the parent process and pid holds the pid of the child
printf("Mah kid's pid is %d\n", pid);
printf("Mine's %d\n", getpid());
} else {
//If it returns zero, you're in the child process
//you can do some preparatory work here (e.g., close filedescriptors)
printf("I'm the child and my pid is %d\n", getpid());
//exec will replace the process image with that of echo (wherever in the PATH environment variable it is be found (using the execlP version here)
execlp("echo", "echo", "hello world from echo; I'm now the child because I've replaced the original child because it called an exec function", (char*)NULL);
printf("This won't run because now we're running the process image of the echo binary. Not this.");
}
return EXIT_SUCCESS;
}