When the car starts sliding. Once the rear end starts to come around, STOP all pedal inputs... Don't try to brake or increase/decrease throttle. Catch the slide first, then let off or let on the gas. Of course, this is very generalized... as with a front-wheel drive, as long as you're in the right gear, you can stomp on the gas to try to straighten the car out (fun off-road), but you're better off trying to correct with steering first.
Then, when the car is in an irrecoverable spin, as Eric says, clutch and brake in. Brake to help the car stop, clutch to keep the engine alive so you can move away from the stop.
Engine braking is a non-issue. In an emergency, nobody has time to shift down two, three, four or five gears while standing on the brakes. You can use engine braking when slowing down gently or going downhill or when your actual brakes fail on the highway... but nothing stops the car as quickly as the regular brakes.
We've done 0-100-0 tests, and clutch-in or clutch-out, there's no difference in stopping distances. The difference is in whether you have to restart the car or not after you've come to a stop.
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I like to tell people, the brakes are not for slowing the car down. They're for stopping it. Period. To save on brake wear and fuel while on the highway or between lights, coast or engine-brake down to the speed you want. One of my biggest pet peeves is people who tap their brakes endlessly on the expressway to bring the car back down to whatever target speed they're trying to hit. Great way to heat up the brakes and glaze the pads... A smart and economical driver will only use the brakes sparingly, which keeps them fresh for when he actually needs them.