To begin, we should probably understand why people get hangovers before we try to treat it. Though it's not completely understood, there are several factors that are thought to play important roles in causing hangovers. Dehydration, acetaldehyde intoxication, and things called "congeners," among others, are thought to be a large part of the reason why some people suffer the nasty side effects of alcohol consumption the next morning.
Dehydration
From the evidence I've seen, this might be the most important mechanism of a hangover, and re-hydrating is also the easiest approach to avoid them (other than not drinking, of course). The process by which alcohol causes such drastic dehydration is detailed a little more here. Basically, the alcohol suppresses the release of vasopressin, which in turn decreases the absorption of water in the collecting tubules of the kidney. Fluid is then free to pass straight through your body, depriving your cells of the watery environment they need, and making you feel sick. In fact, people drinking alcohol actually pee out more liquid than they take in.
Acetaldehyde Intoxication
Well, once you start putting poison in your body, it wants to get rid of it. So, your liver works hard by producing multiple enzymes and products, like alcohol dehydrogenase, acetaldehyde dehydrogenase and glutathione to aid in detoxification of the blood. Alcohol dehydrogenase converts alcohol into acetaldehyde, which is then converted to acetic acid by acetaldehyde dehydrogenase and glutathione. Our body does a fantastic job of getting rid of the toxin, that is, until too much alcohol is consumed. Eventually, the gluthione stores in the liver become depleted, resulting in a buildup of the toxin acetaldehyde. And, as you can probably guess, a long exposure to a toxin won't make anyone a happy camper!
Congeners
Turns out, there's more than just ethanol in alcoholic drinks. Surprise! Byproducts of fermentation, called congeners, are present in varying amounts among different types of alcohol. These range from esters and aldehydes, to the acetaldehyde we just talked about, and, interestingly enough, studies have shown they, too, play a role in hangovers. Generally, the more congeners present in an alcoholic beverage, the worse the hangover will be when consumed. Dark liquors, like bourbon, generally have more congeners than clear liquors, like vodka. And, as expected, studies have found that people suffer much milder hangovers when drinking vodka compared to whiskey. Note: The amount of ethanol is much more important in causing hangovers than the amount of congeners, so don't drink more just because you're drinking vodka instead of whiskey one night!
There are likely more reasons for hangovers than this, but my "cures" mostly address these processes.
How to avoid a hangover
Unfortunately, once you have a hangover, your only option is to basically wait it out. Of course, you should drink water and eat food to replenish the things you lost, but that won't be a fast way to get rid of it. The best (current) methods are from being proactive and avoiding a hangover, not treating it. As a result, my best suggestions will be preventative. Here are some ideas:
Don't drink! Okay, well that's probably not a good reason to read all the way through this, but definitely don't go crazy with it.
As I mentioned earlier, dehydration is probably one of the biggest reasons people get hangovers. So all you have to do to help avoid one is drink water then, right? Well, yeah, pretty much. But wait, don't you excrete more liquid when you're drinking alcohol than you take in? So the water will just go straight through you? Exactly, water that goes right through you won't do the best job in re-hydrating you. That's why the best way to combat this would be to drink a bottle of water about 4-5 hours after your last drink, when the alcohol has less of an inhibitory effect on the release of vasopressin. By this time, the water will be able to stay in your system and give your cells the environment they need. Just set an alarm if you'll be sleeping by that time. I'm sure most people would rather wake up for a few minutes than suffer the consequences of what they did that night. In the morning, just have a nice meal and drink some more water or maybe even a sports drink to replace electrolytes and you should be good to go.
As research has indicated, drinking things with fewer congeners results in milder hangovers than drinking things with more. So lean toward drinking your vodkas and rums instead of your whiskeys and tequilas.
There is also research being done in pursuit of a hangover cure. One study combined the enzymes alcohol oxidase and catalase in nanoparticles to combat the effects of alcohol, aiding the breakdown already performed by the liver. The alcohol oxidase breaks the alcohol down into hydrogen peroxide, which is then converted to water and oxygen by the catalase. The research was performed in rats, and showed promise by significantly reducing blood alcohol levels, as well as alanine transaminase, a biological marker for liver damage. This likely won't be on the market any time soon, so don't get your hopes up.
Drinking more alcohol is not an effective way to treat a hangover. It will only delay it, and might even encourage addiction.
That's about all I have to say, so drink responsibly and don't drink and drive!
References:
Rohsenow D, Howland J. The Role of Beverage Congeners in Hangover and Other Residual Effects of Alcohol Intoxication: A Review.Current Drug Abuse Reviews [serial online]. June 2010;3(2):76-79. Available from: Academic Search Alumni Edition, Ipswich, MA.