Lol

That's purdy *sniff*
Anyways...
Feint really has nothing to do with throttle, clutch kick, braking, or any other input than steering. It's all about steering. Other methods get added to it to make it easier and to manipulate the car properly for the corner. However, feint alone is only a steering method.
What it does is rotate the car. It doesn't make you go faster or slower and it doesn't make you take the corner. It just rotates the car.
How you do it is just turn away from the corner to load the weight on the inside of the car, then you just whip the weight to the outside by steering quickly towards the direction of the corner. This will forcefully make your car rotate. The harder you do it, the more it will rotate. Too much, you'll spin out. Too little, you won't rotate much or you may not even break traction. It does take a bit of practice to get used to how hard you have to toss the car.
This method works very well for cars whose parking brakes don't work so well or for underpowered cars or even fwd cars in which on-throttle methods don't work. It's also a method to use when you are at or near the speed of the corner as it's not a technique to slow you down or speed you up like braking and power over, respectively.
First, learn to get your car rotating. Get used to how hard you have to toss the car to make it break traction. Afterwards, learn to grab the car and control the drift. Once you break traction and start to rotate, you'll countersteer to grab the spin and work the throttle to hold the drift.
It can be done as slow as a large sweaping motion or as quick as a fast jerk. The method is both traction dependent and suspension/car dependent. Since it is a steering method, you will need enough front grip to perform the maneuver fast enough. As well, a car that's heavier will be harder to do quickly but easier to keep the weight moving when you begin to throw it around. A softer suspension requires a slower, more sweaping motion to allow for time to load up the suspension. It requires a good amount of feel to know how the weight is moving around and how much front traction you have to work with.
When starting, the technique does fell quite awkward. It will take a little time to get used to as the method is very different than anything else you've done in a car. Practice, practice, practice.
The nice thing about the technique is that it can be combined with other techniques as stated by others to produce an end result. Sometimes feint isn't enough. Sometimes you may not have the traction or the room to perform the needed feint maneuver, or perhaps you're not at the appropriate speed for the corner. In any case, you will actually combine other techniques to provide the desired result. For example, you can brake into a corner and feint at the same time. This allows for you to come into a corner fast, move a good amount of weight forward, and to allow more front traction(if not braking too hard) to allow for some feint to get the car rotating. Sometimes just a let off of the gas will be enough to get some added front wieght/grip. As well, you can help the feint by doing things like clutch kick or power over to help get the rear end loose.
A good way to practice the art of feinting is to try in on a straight road. Start turning side to side moving from one side of the road to the other. As you tighten your turning, you'll start to get close to the traction limit of the tires. At this point, you can try different technqiues to break traction. You can let off the gas or brake slightly while still turning side to side. You can apply some more thottle to see how that feels and if it breaks traction. You can be more abrupt with your steering to begin to overload the tires and break traction. At some point, the car will start sliding. Once this happens, control the slide and straighten out. You should be able to start and end it comfortablely. Do it again and try to connect more than one slide from side to side just by continuing the same thing. Once it starts to slide one way, steer a little more into it and the car will eventually whip the other way. In time this will turn into a continuous whipping back and forth of the car, a constant feinting back and forth. I'm sure you've seen this in videos where the drifters whip back and forth down a straight section of the road. This is feinting.
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did I type enough?
Hope that helps some.