"The goal of a toes-to-bar is pretty straightforward--to get your toes to make contact with the thing you're holding onto. However, there are a variety of possible ways to accomplish that same goal depending on your strength and flexibility in various systems. While every CrossFitter should naturally find a way to "get it done", it is worth working towards the most efficient movement path for any exercise and here is one way to think about that.
If I'm hanging in a straight, vertical line without moving at all, my feet are about 8 feet away from the bar (assuming I reach a little more than 2 feet longer than my height). To get my feet from that point, furthest away from the bar, to hit the same place as my hands, my goal is to travel the shortest distance with the greatest speed possible, especially if I'm trying to record a great time in a WOD.
Think about a circle, like a giant clock where your hands are at 12:00 and your feet are at 6:00 when you're hanging still. If you are really flexible in your shoulders, you could think about keeping your hips in one place (the center of the clock) and then moving your feet clockwise from 6 all the way up to 12. If you did that, your feet would basically be drawing half of a circle and you'd be going from a 12:30 position to sort of a 12:00. But, that would mean traveling half of the circumference of the circle. Good old geometry tells me that my feet then must travel 1/2 x (2 x pi x r), or 1/2 x (2 x 3.14 x 4), or a little over 12'. But CrossFit is not about math and I don't have to go that full distance if I can instead think of a straight line instead of a circle--I want my feet to travel more like 8' instead of the 12'--that's a 50% improvement in speed and efficiency if you can get there!!
So, step one is to hang straight under the bar and slowly pick your knees up as high as you can, working on your best tuck position by compressing your knee joint as much as possible (i.e. pulling your calves up against your hamstrings) and then using your lower core to "curl" your lower body up with your knees tucked in. This requires a fair amount of hip flexor and lower ab strength and it should be trained on the ground while horizontal to reinforce the right position and mechanics.
When you can slowly get to that position and return your feet straight down until your legs are locked out tight and straight, thinking about the straightest distance possible to the bottom of the circle (not arching or bending or swinging them behind you). Then attempt the same thing with speed. At this point your shoulder angle should be completely open, with your arms by your ears and your head in a neutral position--we're not really pulling with lats or biceps yet, we're just using the lower body and core. We're trying to keep our center of mass directly underneath our hands and not allow it to move forward or back by leaning or swinging.
To get to the next step and be able to get your feet to the bar, you're going to need to do that basic drill and get your knees up to the level of your sternum. If you can't get there, you may start to lean back a little, close your shoulder, and use upper body pull to compensate. However, as soon as you do so you will likely start to displace your center of mass in front of the bar, which means you're going to pick up a little swing. The goal of this technique is to keep your center of mass straight under the bar as long as possible.
Practice doing small sets of 3 to 5 reps with a very fast knee raise to the tuck position and an equally aggressive return to straight down. If you do this correctly, you should finish in a dead hang with no swing forward or backward.
Next, you're going to add in a leg whip, which is executed a lot like a good front snap kick in most martial arts. A front snap kick is done by lifting my knee, pulling my heel to my butt (or compressing my calf to my hamstrings), extending from the knee until my leg is straight, and then returning to the knee up position. The goal is to whip your foot forward and return back to the protected start position as quickly as possible, in a straight line with great efficiency so you stay in one spot and don't leave your leg vulnerable.
If you visualize (and practice) that front snap kick motion, then you have an idea of what should happen next in your T2B. When you have elevated your knees into the highest and tightest tuck possible, you're going to whip your feet up together until you get as close as you can to the bar, and then you're going to return to the tuck position in as straight a line as possible. Then you're going to return from the tuck position to the straight down, 12:30 clock position again in the straightest line possible. I know that most folks are not going to think they're flexible enough, but dynamic/active flexibility may allow you to get there even if you can't normal touch your toes.
An important coaching cue is to think about having a vertical wall a couple of feet in front of you in order to keep your movement path compressed and vertical through all four phases--knees up to tuck, whip to foot touch, return from touch to tuck, and return from tuck to straight line below. Most athletes will want to relax on the return phase and allow their feet to start to travel out to the edges of the circle. This is slower and less efficient and will usually start generating some swing that will make cycling difficult.
WIth fatigue or limited hip flexor strength or mobility, some adaptation can be accomplished by closing the shoulder angle slightly and adding some pull from the lats or biceps. However, this should be kept at a minimum and the focus should be on leaving the upper body still and focusing movement on the legs, lower core, and leg whip/extension to the bar.
In order to meet the normal movement standard of "feet breaking the plane", an athlete can add a slight leg bend after hitting the bottom of the circle, but this is an active flex at the knee to just flick the heels back slightly and NOT a large, open hipped or back arched movement that might create undesirable swing."