Firstly, you need a bike where the handlebars are not loose and floppy. 

Secondly, when you first give this a try, pick a day with little wind and a road which is level. If neither of these are possible, make sure the wind is behind you and you are going down the slope; don�t try to learn to ride "no hands" against the wind, up an incline or down anything more than a gradual slope.

Thirdly. When you are ready to try, ride your bike reasonably quickly and in a straight line... Or at least as straight as possible. Get to a situation when you are not wobbling at all. When you have reached this stage, rest your hands lightly on top of the handlebars and then try moving both hands together just above the handlebars. Keep pedaling not to reduce your speed. If you cannot keep pedaling then make sure that you are not riding too slowly. Keep trying until you find that you can ride no hands for seconds at a time.

Finally. It is then just practice. You have almost cracked it. Try to practice with the same bike everyday. Within a few days your should be riding "no hands" with the best of them. You will find that once you have "cracked it" it comes as easy as riding normally. You can turn corners and even ride more slowly with "no hands", making the bike wobble from side to side.

If you find that you cannot achieve "no hands" after some practice, change the bike, no other solution. Some bikes are just not "no hands" friendly. In my experience, most bikes can be ridden "no hands", but some are much easier to ride in that way than others.   So don't let you get fooled by a bike.

I have taught a few friends to ride "no hands" in this way and most have succeeded within a few practice sessions. One girl took to it so easily, she was cornering "no hands" after less than one hour�s practice.

Good luck.

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I will now add my personal thoughts. I talked about this with Alexandra who totally agree with me: If you find that you cannot achieve "no hands" after some practice, change the bike. Indeed, some bikes are just not "no hands" friendly. More precisely, there is a kind of scale of difficulty depending on the bike that you use... some are very easy to be ridden no hands... and there is all a hierarchy until very difficult ones and some cannot be ridden like this at all.

SO WARNING: this phenomenon is badly known. In my experience, most bikes can be ridden "no hands", but some are much easier to ride in that way than others.   So yes a bike can fool you, and at my knowledge even a brand new one can be dangerous, so don't take in count the good or bad state of the bike, just try another one if you cannot on yours, but of course not on a truely unsafe bike (e.g. with no brakes, and so on... Or make sure that it's well repaired before).

Now, I will add a 2nd Method: for horseback riders: I learned by someone who also ride horses since a long time, that she learned to ride no hands using a tight twine to "hold" the handlebars, and this in order to train to ride horses with long halters.
It's simple: suffice to slacken progressively the twine (I'd say VERY progressively at the beginning), then the self-confidence increasing, let the twine slacken more and more until it's completely released... that's all, I'd recommend this method Only if you ride also horses with confidence.
But the best is to choose the method that you feel!

True story:

I once had the following problem: My front wheel tyre got flat because of a small metallic piece, not a nail, something I couldn't identify, which holed the tyre and the tube. I repaired the tyre by filling the little hole with some silicone gum (not the right trick but at least it works)... But lazy, I decided to change the tube instead of repairing it, although I had the necessary pack to repair the tube in my backpack.

The new tube had the right size except that it was a bit thicker. "Never mind" I said to me, and mounted it. I re-inflated the wheel and set off again. Guess what happend when I wanted to release the handlebars? I almost fell off! Fortunately I quickly grabbed onto the handlebars.

I found that strange, and tried again to ride no hands... NO WAY!! At every try, it was the same, the front wheel was deviating immediately, generally on the right but sometimes on the left, it was depending, But on what? I don't know...

At the beginning I thought that I didn't mount my front wheel correcly, I verified, unmounted and re-mounted it, tried to ride no hands again, BUT NO the wheel was correctly mounted... I couldn't believe that it was the tube... But what else? Anyway, my natural curiosity drove me to repair the tube that, meanwhile, I had put in my backpack.

Once well repaired, I umounted the "wrong" tube and put it in my backpack, I re-mounted the freshly repaired right tube, re-inflated and re-mounted the wheel... Did you guess what happened? I found my bike like it was before, and I could ride it no hands again!!!

I was stunned by the fact that such a small detail could modify the behaviour of my bike! But my conclusion is that what makes a bike easy, difficult or impossible to ride no hands is a kind of incredible tangle of tricks... I've got the proof now.

Be safe!

Riding no hands is not as safe as normal riding, at least not everywhere. Therefore, please do not ride no hands in heavy traffic. Use quiet residential roads, parks or country lanes. 

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