One way is to write a C program that goes:
#include <stdio.h> int main() { unsigned int i = 1; char *c = (char*)&i; if (*c) printf("Little endian"); else printf("Big endian"); return 0; }
Another way is to run a one-liner in your terminal. It goes:
[ "$(echo hi | iconv -t utf-16 | od -N2 -An -t x1 | tr -d ' ')" = "fffe" ] && echo "Little Endian" || echo "Big Endian"
It takes advantage of the magic number 0xFEFF that UTF-16 encoding adds before any text. Look here for more info.