I have noticed that the most effective, simple cure for (normal) hiccups is extremely rarely known, and even when it is known, it's usually not explained properly. I figured this out over the years by simple logic from the explanations in the news of what normal hiccups are, and have been testing it successfully for years. So here it is (basics in bold for easy skimming).
Hiccups are essentially muscle spasms in the diaphragm -- the muscle that forms the "floor" of the lungs and is one of two ways we breathe. Now, when spasms occur in normal muscles, the standard advice is simply to stretch them for a few seconds.
So the easy solution to hiccups is to stretch the diaphragm for a few seconds. The trick is knowing how to do so.
The key is that the muscles that surround our rib cage form the second method of breathing, and when used in combination with holding your breath, can increase pressure on the diaphragm, forcing it to expand downwards, stretching like a balloon under pressure.
So, if you get hiccups, simply take a breath, and compress your lungs via the rib muscles.
It's basically the opposite of sucking your stomach in; your diaphragm should move down, so your stomach should puff out (yes, it'll make you look fat lol). No need to be extreme; just hold it for a few seconds, and release. Now breathe normally. The hiccups should be cured; if not, try taking a deeper breath and holding it longer.
The key is that using the rib muscles to compress stretches the diaphragm more than your control over the diaphragm itself makes possible. It's the equivalent of many types of exercise warmup maneuvers which will typically also bend the muscle more than its own inherent control can do.
The partial version of this is fairly well known, but it's usually just explained as "holding your breath." (As cited on the Wikipedia page.) Just holding your breath is one possible indirect way of causing this, as some people when holding their breath will "accidentally" apply stretching pressure. But this explanation tends not to work because not everybody will habitually stretch their diaphragm when they hold their breath, so these people are left with the impression that holding your breath is just another urban myth akin to "scare me" nonsense.
Actually, sucking in a lot of breath is really not necessary most of the time. Just hold whatever breath you have and compress downward, although the more air inside the better. A normal breathing in is usually enough.
Incidentally, "scare me" sometimes works for the same reason; it will sometimes cause people to suck in their breath, accidentally stretching the diaphragm, but you may as well save yourself the trouble (and the sillyness) by just stretching it intentionally.
To be clear, don't make a big deal about it. It's actually extremely easy.
Sometimes when I've briefly tried to explain this to people, they look all dramatic and try to puff themselves up like, well, a pufferfish, and then think they have to hold their breath until they're blue in the face. (Probably because people are so used to the myth that hiccups are hard to cure, that they think all solutions must be used with gusto.) No, no. Generally just a few seconds will do, and if not, there's no real harm in pausing to take a breath and then stretch it again. It seems to work "cumulatively"; the time spent stretching adds up, rather than the whole thing collapsing so you'd have to start over (though this is hard to quantify just from personal experimentation, so I can't be sure of this part).
NOTE: Wikipedia states on the hiccup page that some forms of hiccups are caused by more serious medical issues, so it's possible this method will not cure all hiccups. Basically, try it, and if it doesn't work, then try something else -- but I find that unlike most "home remedies" that carry that same advice, this one actually works every time I try it.
Drinking water may work as a more long-term fix if water deficiency is causing the original problem, but to me the idea of drinking while your breathing is violently spasmodic seems dangerous, as you might easily take it in the wrong way and have to cough it up. If eating or drinking I try to hold whatever breath I have already and be sure to swallow before trying this.