Yes, I know this - but I think Fezpp was trying to say that the intuitive thing would be to turn left. That is what I was disagreeing with. The intuitive thing for me, and I suspect most drivers, is to do the correct thing - turn into the skid, which in this case is towards the right.
Bill Cosby once said that turning into a skid to regain control seemed to make as much sense as leaning into a punch to minimize the pain. Can’t remember the exact quote (off one of the albums), but that was the gyst of it. Yes, counterintuitive. But as explained several times above, it really does work.
I actually completely agree. My intuition would be to turn right but I was trying to explain a situation where someone’s intuition may force them to turn the other way.
Yes, it is also true for a front wheel drive car if the back end of the car is sliding. This condition is called oversteer (or loose for you NASCAR fans).**
A front wheel drive car can act differently than a rear wheel drive car in an understeer condition (that’s tight or a push for the NASCAR fans). This is when you turn the wheels and the front of the car slides. This can happen fairly easily on slippery roads. It can also happen at high speeds such as on a race track. In this case, your front tires have exceeded their traction limit (slip angle). You need to reduce the amount of traction that you are trying to use from the tires.
With front wheel drive, hitting the brakes can be bad since that also uses some available traction. Hitting the gas does the same thing. In fact, you can play around with this on a snowy day. If you try this, make sure there is no traffic around, I’m not responsible, etc.
Stop at an intersection. Slowly proceed forward and turn either left or right, keeping traction. Now press the accelerator until you feel the tires start to spin. Your car will immediately quit turning and start heading straight. Just let off the gas to recover. You can repeat this same experiment using the brakes. It will do the same thing if you use too much brake. One last way to cure the problem is to just reduce the amount your wheels are turned (make a wider turn in other words). Just don’t panic and make sure there is nothing you can hit before you try it. To sum up, with understeer and a front wheel drive car, let off the gas or brake or turn less.
Understeer with rear wheel drive can also be cured by letting off the gas. Braking can again be bad especially since most passenger vehicles get more braking from the front wheels. However, you can also cure an understeer condition with a rear wheel drive vehicle by hitting the gas. What you are trying to do is reduce the traction of the rear wheels, allowing the front tires to grab again. You most likely will never try this on the street, but it’s a common practice on a race track.
As far as the original “steering into a skid” thing and racing, it’s used all the time too. Watch some dirt sprint cars to see this in a highly exaggerated way. The hardest part for me when I get my race car loose (back end is sliding) is that I actually have to turn towards the concrete wall around the track to save it. Things can get kind of anxious as you steer towards a concrete wall while traveling at a high rate of speed!
**If you have read the whole explanation, you can see that it may help to hit the gas with a front wheel drive car when you are in an oversteer condition. These are the kind of things I try out when I’m bored on a snowy road and no traffic is around. 
Reading posts to this thread is why I like to take new drivers out to the high school parking lot after the first snow and let them get used to skid recovery. An ambulance or fire truck getting akimbo on the road is something I want the driver to recover from instinctively, should it happen.
Plus, under controlled circumstances it’s kinda fun to play in the snow with big trucks! 
The reason your car was fishtailing was probably because you released the gas pedal, or even worse, you applied the brakes. You see, steering into the skid (or counter-steering as is the correct term) is not always enough. You have to keep pressing the gas pedal too. If you release it, the weight transition will make the rear end lighter and you’ll end up doing a 180[sup]o[/sup] turn.
I, too, hate the terminology “steer into a skid” and it caused me hesitation problems when I was first learning to drive. I think it makes more sense to think of it in terms of rotation. Say that forward is 12:00. When you skid, your car starts rotating towards 3:00 or 9:00 (although your direction of travel stays roughly the same). You always want to steer back to 12:00.
I grew up driving in bad weather so I’m usually pretty good at dealing with it. But one time I was driving down a steep hill in a rain. I came to a stop sign so I started braking and I went into a fast couter-clockwise skid which ended in me blowing the stop sign and then facing backwards on the road, still moving in the original direction. I should have used the gas pedal to arrest my downhill motion, but instead I braked. By the time the car stopped I had gone up the curb and was sitting with one wheel in the devil strip. I looked around and I had managed to stop about a foot away from a telephone pole. 
That evening, my friend Allan came home looking frazzled – when I asked what was up, he explained that while going through that same intersection he did the exact same thing – but he hit the pole. I, wisely, kept my mouth shut. 
–Cliffy
Could I assume that keeping the same throttle position while simply RELEASING the steering wheel would be the same as steering into the skid?
Absolutely not. You have to turn the wheel in the direction you want to go. Releasing the wheel and maintaining power will put you into a spin. But let’s start at the beginning.
There are two problems with the “steer into a skid” advice, namely that the meanings of “into” and “skid” are not eminently clear.
Let’s start with skidding. Only Rogue Racer has alluded to the fact that there are two distinct kinds of “skid.” The one most commonly thought of is oversteer: the rear end of the car swings out. This is usually induced by applying too much power while the front wheels are turned, often in wet conditions.
The car is rotating and to regain control you have to turn the front wheels in the direction you want the car to go. If your rear is swinging out to the left, you have to turn the steering wheel to the left. This is what is properly meant by “steering into the skid.” But I’ve talked to people who thought (and I think this is what Bill Cosby thought) that “steering into” meant "in the same direction as the rotation, " i.e. to the right, which is wrong.
In these circumstances, many people tend to overcorrect, and can save it from the original skid, only to lose it in the other direction. If they’re lucky, they may just swing the rear back and forth a couple of times before getting it to straight. Do not jerk the wheel suddenly. You have to be smooth.
BTW, if you are in a spin and go past 90 degrees (your direction of travel is straight out the side window), just hit the brake (and clutch if you have one) hard, because you will not be able to bring it back.
The other form of skidding is understeer, which is most commonly encountered in icy and snowy conditions. You turn the steering wheel, but the car keeps going straight. This is not the time to think of “steering into the skid.” In fact, that advice makes no sense in this situation. This is also the time when you have to do something completely counter-intuitive, namely stop turning the wheel in the direction you want to go, and turn back towards straight. Your front wheels are turned and are sliding; they have no traction. Turning them further in the direction you want to go will not help. Unfortunately, that is the very natural inclination of most drivers: the car’s not turning, so I have to turn the wheel more. Actually, you have to straighten the wheel until the front tires start to grip again, then slowly turn back the way you want to go. If they lose grip again, straighten up again.
Without training in this technique, most people never figure it out on their own or do it in an emergency. They just keep turning the wheel, or worse, turn and brake. When you are in understeer and brake, you transfer weight to the front and take it off the rear, and can put yourself in a spin, because the front wheels may start to grip and your rear will be light. Slamming on the brakes on ice will usually not help, since you can’t control a car when all four wheels are sliding.
Finally, the reason people often hit a tree in an accident is because they were looking at it. Hand-eye coordination is a mysterious thing, and works much better than most people realize. Believe it or not, you will go where you are looking, and when you lose control and see a tree that you are worried about hitting, you naturally focus directly on it, and as a result, drive right into it. You have to look at the space between the trees! Hard to do, but vital.
–commasense (race driving instructor)
On “over steer” (I am neither correcting anyone who has posted here nor claiming expert status).
Everyone who has driven a road car and gotten it out of shape has felt this. You get loose, the back end takes off, you correct, then the car snaps back the other way (but less, hopefully), you correct the other way, and, pendulum-like, make consecutive opposite corrections in a gradually diminishing progression (hopefully).
When I started racing WKA Karts (unsprung go-kart racing thingies), I found they behaved entirely differently when they broke loose. Assuming you could correct at all (they tend to break loose HARD when they go), there was little “over steer”, you just kinda steered out of it.
When I asked about it, this is the explanation I got (no cites). A road car is sprung. Unless you are on a frictionless skid pad, the tires will provide friction in a skid, and the body will roll and load energy into the suspension (springs, shocks) on the side you are skidding into. When you steer out, even if you provide the EXACT amount of steering to correct and no more, as soon as you stop the loading on the suspension, it will unload the stored energy in the springs/struts/shocks in the opposite direction and upset the chassis. I was told that, to a degree, “over correcting” was unavoidable due to physics. Of course, you could always over correct on top of the physics, in which case you got to meet Mr. Ditch.
I also thought this was just common sence.
And one more form of skidding. Four wheel drift. I drive mountain passes every day. In winter I deal with LOTS of ice and snow. In four wheel drive, four wheel drift is more common than in two wheel drive. I generaly treat it like any other skid (keep the wheels pointed in the direction of travel). Sometimes though, it can help to turn your wheels out of the skid (a little bit) and apply power (4X4 only).
Every situation is different, and only experience and gut reactions will really help. As others have said, I always thought this was just a common sence reaction to your car. Surely nothing you would have to think about. If you DO have to think about it while in a skid, It’s probably to late anyway. Your best bet then is practice in a controled environment.