1. Get a cup/glass/bottle of water.
2. Take a small sip about every 5 seconds for 30-60 seconds.
3. Your hiccups should be gone.
If you want to make it a party trick and do this for a friend, make sure you're the one holding the glass and putting it up to their mouth every 5 seconds or so. Most people don't know how to cure hiccups, so it's actually pretty fun.
I have self administered this several times and it has worked every time.
Why I think it works?
Many other solutions involve drinking water, taking sugar, holding your breathe, etc. You just need some way to control your breathing to settle your diaphragm down.
Step 1: From the Archives of Time Magazine - Monday, Sep. 06, 1948
Almost everybody, except a doctor, thinks he knows a sure cure for hiccups. And sometimes the home remedies work.
Theodore L. Syvertson, of Pasadena, a 69-year-old retired building contractor, had hiccuped almost continuously, once every ten seconds, since November 1946. He lost ten pounds, spent nine months in hospitals, had consultations with 60 doctors which did him no good. Last week he tried bending over at the waist while drinking water from the far side of a glass. Halfway through the second glass, his hiccups stopped.
Pauline Lucas, 31, of Waynesburg, Pa., was hiccuping last week 10 to 25 times a minute, as she has since last Feb. 23. She has not tried Syvertson's method. Suggestions received in 8,000 letters have included such standard remedies as breathing in & out of a paper bag and eating ice cream. Doctors at Greene County Memorial Hospital have tried sedatives, anesthesia, benzyl benzoate (a relaxing drug), quinidine sulfate (a quinine-like drug used to regulate abnormal heart rhythms), amyl nitrite (a drug used to treat angina pectoris).
The doctors are also considering the new drug myanesin (TIME, July 12), and may suggest crushing one of the patient's phrenic nerves (TIME, Jan. 27, 1947) to stop the spasms of the diaphragm that cause the hiccups. Miss Lucas, whose weight has dropped from 129 Ibs. to 85, is willing to try almost anything.
Juniata McMichen, 19, of Atlanta, tried a variation of the scare technique. She took an hour-long ride in a stunting airplane, including a dive from 10,000 feet. It was her first plane ride and she was "almost scared to death." But it did no good; she climbed out hiccuping six a minute. Doctors finally cured her by crushing a phrenic nerve.
Here's the article.