Easy! Just disbelieve them!
Say the following out loud:
Hiccups are a spasm of the diaphragm
A spasm is defined as a random tensing of a muscle
If the hiccups are random, they will not appear in a pattern
Therefore these hiccups do not exist.
If you hiccup part way through, you have to start over. Once you get through the whole thing, your hiccups are cured.
Ok, now hear me out. This isn't just a joke, I've had at least two people that I hadn't seen in years call me up and say, I need you to tell me the hiccup cure, now!
My best theory as to why it works, is that you're focusing on repeating the words fast enough, and/or it makes you breath irregularly and breaks the hiccups. Or maybe it's just the magical power of the mind! Oooooooooh!
Oh. It never works when you're drunk. I don't know why, but drink hiccups seem to be resistant to the method.