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My experience is that you don't use them. They work poorly, which is why they are generally being replaced with newer more efficient dryers or removed altogether.

In theory, you can use them by pressing the button, then rubbing your hands together underneath in the airflow. If you're extremely patient and do this for long enough, you should eventually wind up with dry hands (not that anybody has ever waited this long). The dryer runs for such a long time precisely because it takes a long time to actually use one to dry your hands.

In practice, you use them by pressing the button, finding the air either too hot or too cold and trying to move your hands up and down so as to find hot air without burning yourself, realizing this will take forever, and either giving up or wiping your hands on your pants. More experienced users will typically short-cut the process and skip directly to the final step.

Don't just take my word for it though; complaining about these old hand dryers was a hot topic in the '90s, and earlier:

• Blowing off steam about those useless hot-air hand dryers in the restroom


• 
  Electric Hand Dryer Takes Step to Blast Paper Towels: "The electric hand dryer is the public restroom's version of the Yugo: slow, ineffective and easily mocked."


• 
  Dave Barry: "Electronic restroom hand dryers are miraculous labor-saving devices that work by shooting out a special kind of air, made from compressed sneezes, that actually makes your hands sticky without getting them dry."


• 
  Gerald Nachman, The New York News (1975) - "In fact, just to avoid the offensive task of machine drying, people have given up washing altogether"


• What are Hyenas Laughing At, Anyway? - David Feldman (Google Books excerpt, full text not online)

You might also find interesting this Atlas Obscura article:
The Weird History of Hand Dryers Will Blow You Away

The aim is to maximise the surface area of the water on your hands, so keep spreading the remaining water all over your hands, especially to those parts that have already dried.

Tease out the water between your fingers as this water is often the last to dry out.

• Before you start, shake water off your hands. Faced with a drier I know to be feeble, I use a flicking motion where I tuck all fingers under the thumb then spread them wide, several times. Do this over the sink, not the floor ;-)




• While under the air, your hands should be in motion at all times. There are two motions to combine/alternate.




• Motion 1 is to cup the ball of your thumb in the fingers of the opposite hand, then slide those fingers around the back of the first hand, then along the backs of the fingers. Then cup what was the "opposite" hand in the fingers of the first hand, repeat in reverse. This is basically a classic "hand-washing" mime.




• Motion 2 deals with the fact that the classic "hand-washing" mime doesn't separate your fingers: you need to spread and interlock your fingers, rubbing the sides of the fingers against those of the opposite hands. I generally need less of this than of Motion 1.




• Be alert to the feel of the air on your hands: you don't want all this cupping to mean that your hands are shielding each other from the air half the time. Don't clench them together, keep them fairly open and loose, and avoid the temptation to close the "inner" hand into a near-fist while the outer hand rubs the back of the fingers.




• Some time after you're getting really bored of this, you'll feel your hands go quite quickly from sliding wetly over each other, to feeling more friction. At this point they are almost dry, but actually still a little moist to the touch. If you aren't planning to shake hands with anyone immediately you walk away, this is probably dry enough, otherwise you might want to stick at it even longer.




• If you're wearing rings then the skin under the ring pretty much is going to stay damp. Tough.

The goal is that every part of the surface of your hands is regularly brushed by another part of the surface of the opposite hand. That way, anywhere that water might otherwise collect is disturbed, and the water spread onto other parts of your hands that are drying. Beyond this principle, the exact details can be whatever works for you.

In practice, I agree with Zach that it's generally not worth the bother. Pro-tip, I find that the shirt in the small of my back is a more inconspicuous place to dry my hands than my trousers. But then, I often wear a loose shirt or a sweater over a T-shirt.

The air that comes out is often either too hot or too cold

Cheap hand-dryers are hardly going to optimize your comfort. If you aren't in pain then just keep at it. If you are in pain then move your hands down (further away) or give up entirely. Even cold air has some drying effect, but if it's clearly taking longer than you have patience for, bail out.

the period during which the air comes out is way too long

Maybe I'm missing something, but if your hands are already dry and the air is still blowing you've won. Just leave.

Finally, if you're worried about the hygiene of the thing then carry your own clean paper towels, and/or apply an evaporating hand-sanitizer after washing and drying your hands. For that matter, if you're worried about the hygiene of hand-washing then reading techniques for scrubbing for surgery is instructive (I'm not bothered myself, but I do get bored at the dentist's and they have a wall chart at mine)

Not that I find the new air-jet dryers much better, but if I find one of these old models in a bath room and there are no paper towels there, I usually seek a toilet cubicle after washing my hands and grab some toilet paper to dry off.

I share your frustration with such dryers, which to me are strictly inferior in almost every way to simply providing paper towels.

As indicated by Sam, part of the trick is to not have very wet hands to start with. And, as noted by Zach, one usually winds up using a slightly less-sanitary method of drying the hands. Personally, I split the difference. I know that I'm not going to be able to keep my hands out of my hair, so after washing up, I run my hands through my hair, simultaneously removing water and using said water to help slick my hair back down, then I use the dryer on my now-only-slightly-damp hands, which works much better. I'll typically do the same thing with paper towels so that a single towel is enough to dry my hands.

But wait... doesn't running your hand through your (presumably) dirty hair negate the benefits of hand-washing? Well, unless you work in a clean-room, or in a food-preparation job, the odds are good that within minutes of washing your hands, your handling dirty keyboards, doorknobs, coffee-maker handles... the speed at which your body is recontaminated with bacteria is pretty shocking, although the fact that most of us are covered with e. coli and suffer no ill effects also points out that our bodies really are pretty good at this whole "protecting us from illness" thing.

Your feeling that the period the air comes out is too long and the inability to get your hands completely dry are directly related. Yes, it takes more time to dry your hand with hot air that with a towel. You need to rub your hands for about 1 minute in hot air to get them dry.

Just avoid using the toilet 5 minutes before your train/bus/etc. is leaving, or when your name is already being called at the airport gate, when you don't have a minute to spare. You'll have the occasion to use the bathroom in the said train/bus/plane.

Shake, rub, turn while shaking and rubbing. The little known secret is a certain hop on one foot that completes the drying action -- wait, it is not. I mention the hop because there is actually a secret: once you've warmed and partially dried your hands this way a little wipe on the clothes, bachelor style, will very quickly get your formerly wetted skin to a very near-dry condition. Voila, accomplished (or as some of my British friends would say, 'Result!')