How do you clear the console screen in C?

Well, C doesn't understand the concept of screen. So any code would fail to be portable. Maybe take a look at conio.h or curses, according to your needs?

Portability is an issue, no matter what library is used.

printf("\e[1;1H\e[2J");

This function will work on ANSI terminals, demands POSIX. I assume there is a version that might also work on window's console, since it also supports ANSI escape sequences.

#include <unistd.h>

void clearScreen()
{
  const char *CLEAR_SCREEN_ANSI = "\e[1;1H\e[2J";
  write(STDOUT_FILENO, CLEAR_SCREEN_ANSI, 12);
}

There are some other alternatives, some of which don't move the cursor to {1,1}.