go to chinatown. better yet, go to flushing. find a spot that seems like it serves dumplings. ask them for a seat. if they answer in clear English without an accent, *run*.
order soup dumplings. they might be the first thing on the menu. they'll probably be pork-based.
you'll get a basket of dumplings, a big spoon thing, a plate, and some chopsticks. Pick up a dumpling with the chopsticks and put it in the spoon. poke a hole in the dumpling with the chopsticks. super hot soup will pour into the spoon. let that happen. then, after you think it's probably not going to burn the shit out of your mouth, eat the dumpling and drink the soup.
do not leave NYC without enjoying this.
unless you keep kosher, in which case, I have other, less good recommendations.