Speed wobble (aka death wobble). Google those two terms and you'll get a whole heap of information. Unfortunately, a lot of it is proffered by people who've never experienced speed wobble, but can't resist pitching in. Unusual, that, for the internet.
First, let's be clear about what is it we are talking about. Speed wobble is an uncontrollable front end wobble of the fork, steerer & bars, that can appear from nowhere and become (very quickly) so violent that you think you're going to be thrown off your bike. Usually it happens at speed on a descent (although it happened to me once on the flat when a moped I was drafting behind brake tested me pretty hard). Scares the living bejesus out of the rider. I used to get it on a Giant TCR I once had. Every descent, bang on 54 kmh. That's speed wobble. Any pale imitations not accepted.
Secondly, let's get straight to the answer: how do you stop it? There is, AFAIK, tried and tested immediate remedy. Lift your backside ever so slightly off the saddle, and/r clap the top tube between your knees. I have heard of a longer term solution as well: grip the handlebars very lightly. This one is obviously counter-intuitive when they are shaking out of your grip, but the idea is not to grip them too hard in teh first place. This, I gather, is a solution that a rider needs to work on over time to perfect.
Thirdly, it's all very well treating the symptons, but what's the cause? There are a million and one ideas floating around the internet. My favourite (wrong) one is a loose headset. What is obvious (at least to me) from the symptons is that speed wobble is a resonant vibration in the bike. Unlike a standard vibration, which dies away over time, a resonant vibration grows in amplitude over time: each input back into the system feeds the vibration. The "solutions" above suggest that the vibration is bouncing off the rider's contact points, and being amplified by them: remove the reflective surface (the backside) and the vibration dies away.
The question is what is feeding it in the first place? The obvious place to start is a moving part rather than a static part. My personal ideas (which I have never tested with any sort of rigour, or proved to be accurate, so take with a pinch of salt) concern the front end: (a) is the front wheel evenly placed in the fork dropouts? Spin a vertical wheel in your hands, holding by the QRs. Spins nicely when its vertical. Now tilt it off vertical slightly. Big forces at work - you can feel them immediately. (b) is the fork even? There's a fork manufacturer (can't remember which one) that has a section on its website that explains that speed wobble is attributable to the arms of a fork not being precisely the same length (which is their unique selling point). This fits in with (a). (c) Are the handlebars pointed forwards? This is the first think I remember fixing on a bike when I was a kid. You look down as you're riding in a straight line, and notice that you bars are pointed ever so slightly to the left or right. Never seems quite as easy to get them true as it should be. But in principle, I suppose if you were unwittingly trying to get the bars true on a descent with rigid arms, you'd push the front wheel out of dead ahead. (d) (a longshot, this one) one hand is exerting more pressure on the bars than the other. Again, another way of creating a marginal wheel imbalance.
Now maybe the majority of riders suffer all of these problems, but the vibrations that they each create serve to cancel one another out, so the vibration never gets going. I have no idea.
One final idea (again, never tested, so pinch of salt) is this. The resonance is of part of the frame. However, it seems to me that the resonant frequency may depend on the dimensions of the entire structure, and the rider weight (eg an 80 kg rider gets speed wobble at 55kmh. Would a 50 kg rider get it at the same speed, on the same frame, identically set up?). If so, then a small change in set up *may* adjust the resonant frequency. I have in mind swapping the stem for the next size up, or adjusting the saddle height marginally.
Hope that helps. Just remember: just because you read it on the internet doesn't mean it's true.