In a nutshell, LFB is useful for
1. Slowing down the car, just like "classic" Right Foot Braking, including for tail-braking and everything, but without any lag between throttle and brakes. This let you brake harder, sooner (so you can ultimately brake later) and reduces your overall reaction time, which in turn makes you more confident: if you run a bit to fast already and the corner is tightening a bit, you can quite easily slow down a bit an even throw the car sideways in the middle of the corner if needed, see below. When you first learn the technique (and begin to master it) it actually makes you slower: it's so convenient and reassuring that you tend to brake too much and too often. How does it work? When you lift the throttle abruptly, the car’s nose goes down (the entire car slow down, of course, so there is a "weight transfer" towards the front, but if you look closely, there is a very short and abrupt nose-dive that only lasts an instant). The idea is to “catch up with the brakes” as the front of the car still goes down, so you benefit from increased load at the front (resulting in more normal force on the road surface = more grip) at the beginning of the braking. As a result you brake harder sooner and you don’t lock the wheels. With the right-side foot, it’s too late when you reach the brake pedal: the car's nose is already slightly on its way up (the abrupt nose-dive effect is gone in about a tenth of a second, two at most) and there is less load on the front already, just when you need it most… Stiff suspensions make everything happen quicker. To use LFB as your main (or only) slowing down technique, you need a gearbox that let you downshift without using the clutch at all (aka a "dogbox"). If you have a sychro gear box (like all road cars have) then this technique is mostly limited to situations where you don't need to downshift (but I've seen Pentti do a Scandinavian flick in 4th gear, then do 4-2 with the clutch while the car was still sliding, just before accelerating out of the hairpin). Now be prepared for a little shock: Flying Finns never use the clutch for downshifting! With a dogbox, they always use the clutch for upshifts, because "when accelerating, you cannot afford to miss a gear", but never for downshifting. Look carefully at what Tommi Mäkinen does on a Group N production car with a H-pattern dogbox. Now a small tip: always slow down first, a lot, then downshift: simply keep the engine from under-revving, so you are at the beginning of the power band when reapplying the throttle, not already past the red line... it also makes it easier on the gearbox dogs (and the valvetrain). In other words: slow down with the brakes (and by throwing the car sideways), not with the engine. It takes a lot of time and practice to be able to modulate and apply those "20% slip" maximum braking with the left foot at any speed, but the benefits are worth the effort.
2. Throwing the car sideways: it starts with an accelerating car with the throttle floored, usually in mid or high gear (3rd, 4th and up), which is the normal situation in rallying. Whenever it’s time, start with a smooth steering input in the direction you want the car to turn while getting abruptly off throttle, then immediately apply moderate pressure on the brakes with the left foot, all in a split second and in a smooth overall motion, but in that order (NO significant simultaneous throttle and brakes). The rear starts to slide because of the steering input and the abrupt weight transfer to the front. You stop it from sliding by easing off the brakes and re-applying some throttle, with a little less steering input or perhaps a little counter-steering, but in any case the steering inputs should be light. You increase the sliding (yaw angle) by easing the throttle and applying more brakes, and perhaps with a little more steering input (brakes and throttle controls the amount of load transfers on the front-rear axis, steering sort of controls the yaw angle change rate). The key word here is smoothness. Throttle and brakes always move in antagonist manner, never brakes + throttle at the same time, you trade one for the other (of course there is some overlap, but the pedals really always move in opposite directions: when one goes up the other goes down and vice-versa, watch Tommi Mäkinen explain his footwork with the hands). The whole setup takes about 1 second and you find yourself sligthly oversteering, with the throttle on and the front wheels almost straight, pointed at what will soon be your apex. From there it's a matter of going through the corner while maintaining both the speed and the slight oversteer, by modulating the throttle and brakes as needed and applying minor steering corrections. The car goes round the corner with very little overall steering input and lots of throttle (listen to Tommi: "wheels completely straight and full throttle in the corner"); this technique allows you to take corners fast when grip is low, as you depend much less on front grip to turn the car, so it's a great technique to help overcome understeering and you are using all 4 wheels through the corner instead of just the outer-front one. While most effective on 4WD cars, the technique works mostly the same for all type of cars with slight variations for FWD cars, see notes below. Beware that it only works well from a certain speed, say from 60 to 70 km/h (40mph) and up, depending on the grip conditions. In fact, it usually starts working well when starting from a speed quite higher than the speed at which you could ever take the corner "normally", on the given conditions. Bottom line: you'll crash if you don't know what you are doing, and you need true determination to succeed with this technique!
3. Throwing the car sideways in a pendulum motion: The Scandinavian Flick (sometimes used on mud, snow or gravel but probably never on asphalt). It consists in using the above technique to throw the car sideways in the opposite direction while still moving, overall, in a staight line: steer slightly in opposite direction, lift off and appy the brakes in a split second. When the car starts to slide, steer to keep it going straight with a bit of opposite lock, some throttle and less brakes. You are actually driving sideways-in-straight-line here, perhaps for 10-15 meters/yards, sometimes more, with subtle steering inputs and a bit of brake/throttle modulation - this is extremely hard to do right, especially considering that the car is moving at high speed, perhaps 100km/h (60 mph), sometimes much more. Just before the turn-in point is reached, release the brakes and apply some light throttle while steering a bit more in the corner's direction, and wait... The car has slowed down by now and eventually the rear wheels will bite as you loaded them a bit with a little throttle and released the brakes. Just after the car started swinging back, release the throttle and reapply a (smooth) bit of brakes almost the same instant: it will pick up rotational speed quickly in the corner's direction and swing (flick) with some determination. Just before you find yourself oversteering in the proper direction, release the brakes (you can use the clutch to engage the proper gear now, if you need to, you'll do so while the car is still swinging), then apply throttle to seat the rear, and modulate as needed to control the yaw angle, as described above, while keeping the front wheels in the direction you want to go. This is NOT easy to do. The Scandinavian Flick let you slow down the car quite effectively almost regardless of the grip level and the pendulum motion makes sure it will turn, even if the grip is very low. This is the ultimate anti-understeer technique but use with moderation, i.e. only when the grip is so low that the car would not turn otherwise. Note that it's a relatively long operation (NOT a quick steering input in opposite direction right at turn-in!), you have to start the whole manoeuver with a lot of anticipation, depending on the speed and grip, perhaps 30-40 meters/yards (sometimes much more) before the corner's "normal" turn-in point, also note that it only works at speed, say 4, 5 or even 6th gear for best effectiveness... The most difficult thing to overcome: if you take the corner normally - you know: tail brake then squeeze the throttle on the perfect racing line - you will reach a point where you crash with terminal understeer if your entry speed is too high for the grip level and the given corner. The problem is that you have to go quite substantially faster than that for the above techniques to start working effectively, i.e. to be able to set up the car with the proper level of oversteer and go through the corner safely (and certainly quicker). Needless to say, you need a lot of confidence and training, even more to be able to do it consistently. Keep in mind that this pendulum technique was developped to drive fast on ice, snow and gravel, and that there is no miracles (for example driving fast on ice without studs is hopeless, or if you present yourself way above the "right" speed for a given corner). Pendulum techniques make no sense on asphalt, where (left-foot) tail-brake oversteer and clean, smooth, unspectacular lines are much more effective and quick. The perfect illustration: Mikko Hirvonen on snow. Watch this carefully a few times, then re-read the above.
4. Settling down the car: a bit of brakes helps settle down the car when landing from a high-speed jump with the throttle floored. This is essentially the only case where you'd briefly apply significant throttle and brakes simultaneously, but only for an instant and usually in straight line. It helps stabilize the car when landing, say, above 160km/h (100mph) from a jump. Listen what Marcus Grönholm says about this technique: "..even at full throttle I'm a little bit using the brakes to stabilize the car... not much, just a little bit" (he's driving on gravel near 200km/h (125mph) here).
It's not easy to combine 1 and 2, as 2 is much more effective when starting with the throttle wide open. Still, you can steer somewhat early (before the normal turn-in) and let the car oversteer a bit by the time you reach the theoretical turn-in point. To do that you need to release some brake pressure, slightly before the end of the straight-line braking phase, to gain a bit of directional ability (remember the traction circle: you cannot really turn if already under maximum braking) and the car will get sideways as there is little load (and some remaining braking force) on the rear. The whole point is to create some slight, deliberate oversteer to make sure to be on the safe side, i.e. not understeering. The tires will give you their best with a few degrees of slip angle so a little oversteer actually helps the cornering force and let you go through any corner faster (a little is, say, 5-7 degrees of yaw angle, just to give a number, a bit more as you go slower and/or there is less grip available).
FWD notes: On front wheel drive cars, you can leave a little throttle on (maybe 10%?) during the entire braking phase, this helps avoid locking the front wheels and stalling the engine, which spells your death on slippery roads as even releasing the brakes completely will not cause the engine to restart, you'll end up with both front wheels locked and no power steering, way past the turn in. Needless to say, you will NOT make the next corner. Keeping some throttle conteracts the brakes a little and can actually be useful for FWD brake modulation on very slippery roads as it makes the wheel locking point "softer". You can also dynamically alters the brake balance if you modulate some slight throttle while braking: a little more brakes with a little more throttle is like biasing the balance to the rear. Impossible to do this when braking with the right-side foot... Raising the idle RPM also helps and acts as a cheap anti-lock system. You don't need the engine brake anyway, today's brakes are very effective so don't fear raising the engine's idle speed some 500-800 RPM above normal if you use your left foot for all braking (with right-foot braking the diminished engine brake is a bit scary). Also on FWD (only!) you can leave some brakes on (again, perhaps 10% or less, just a tad bit) during the entire corner phase, and fade the brakes out up to the very exit. This helps the front diff (= more traction out of the corner) and also removes a bit of rear grip, helping the car to turn. Do it very lightly, there is absolutely no point in getting heavy on the brakes and the throttle at the same time, on FWD you'll end up locking the rear wheels completely (or the front wheels on a RWD car), losing some control in both cases. On a 4WD you are just burning the brakes. I've seen some RWD drivers brutally slam the brakes with the left foot to lock the front wheels - and understeer - as a last resort to avoid a spin during a stupid (and slow) so-called "power-oversteer". It works, but this is not what LFB is about. On road-going turbo cars you might want to apply some throttle early, while still (tail) braking, to help the turbo pick up some speed and reduce the lag. On proper rally cars with turbocharged engines the anti-lag system does a much better job at keeping the turbo spinning, so no such trick is needed.
Watch a master at work (Colin McRae on YouTube, explaning left foot braking). Scandinavian flick at about 1:30 in this other video. Also don't miss Tommi Mäkinen's footwork on wet asphalt (starts at 2:10). Hopefully you'll appreciate the smoothness. By the way that car does 0-100 km/h in about 3.6s on the wet...)
Finally, a word of caution: by all means, DON’T TRY THIS AT HOME. Don't trust your (and other's) life on information found on the internet! Take a one-to-one course with someone who really know what he’s talking about (usually a Finn...), then practice, practice more, and go back take a second course, maybe a couple of months later, THEN raise your ambitions. Once you have learned it you can never go back, right foot braking is simply far too dangerous :-)