Tango walk is done by two partners chest against chest in the embrace. The man walks forward, the woman walks backward, and they must walk with matched posture, pace, alignment, CBM, dissociation, lilt, rhythm, etc. in perfect coordination, balance, harmony and elegance. Many students cannot walk well because they don't have the needed muscles, flexibility and techniques, their legs and feet are too weak to maintain balance and stability, their postures and habits are not up to the standard of tango, and their personal praxes conflict with each other, causing disharmony and instability in the walk.
There are more exercises in tango designed for women than for men, just like there are more fashions, shoes, jewelry and cosmetics designed for women than for men. Which is not surprising given the importance of beauty to women and the fact that, while the man leads the woman in tango, it's the woman who beautifies the dance. (See The Gender Roles in Tango.) How women walk, therefore, matters more than how men walk in tango.
In order to walk well, you first need to develop muscles that enable your feet to suck the floor and stay very grounded in the walk. Dancing a lot certainly helps. Exercise and workout can also be beneficial. One exercise that I found particularly helpful is demonstrated by Vanessa Gauch in the following video.
In tango, women mostly walk backwards, which is difficult because that is not how they normally walk. To learn to walk backwards, you almost need to start from toddle. The following video, demonstrated also by Vanessa Gauch, can help you understand how it should be done.
It is important to point out that the embrace affects the walk significantly. Walking in an A-shaped frame is very different from walking in an H-shaped frame. A women using open hand hold in the dance cannot stretch her leg back far enough, because without leaning on the man it is hard to keep balance on one leg while outstretching the other leg. Here is an example.
The two teachers are competent dancers, I believe, but the H-shaped frame they used in the exercise hampered their performance. In comparison, walking in close embrace, or an A-shaped frame, is much more stable, balanced and elegant, as illustrated in the following video by Jennifer Bratt and Ney Melo.
Good tangueras all use the hip to move the leg, without exception. Here is another excellent example, danced by Mariana Montes with Sebastian Arce.
Keeping your own balance is the key to be weightless
As comfortable as it is to lean on your partner, you need to keep yourself light and not become his burden. This means you have to keep your own balance by bending your standing leg when you outstretch your free leg, as explained by Vanessa and illustrated by Jennifer and Mariana, so that most of your weight is carried by your standing leg rather than on him. This will also allow you to outstretch your free leg farther. Personally I found that when a woman leans lightly with her chest rather than heavily with her stomach on me, she becomes lighter.
You stretch your free leg back until the thumb of the foot touches the floor. At that point you should not just wait there for the man to push you. Rather, you transfer weight to that leg by pushing with your standing leg. Failure to do that is the reason why some women are heavy in the walk. Be careful, though, not to self-propel so hard as to lose the torso connection with the man. You only push with enough force to make yourself lighter, but remain your leaning position and hence the connection with him. The following clip illustrates the correct way of doing it.
Walking with bent knees is inelegant, which is a common problem for beginners. Although you need to bend your standing leg down a little bit in order to outstretch your free leg farther, the free leg must remain straight until the transfer of weight to that leg is completed. In order to do that you should not use the thigh to move the leg, which is the cause of the curved leg. Rather, you should lift the hip and use the hip to swing the leg so the leg remains straight, and you should keep the leg straight as you transfer weight to it. Keeping the knees straight makes the dance look more elegant, as this video shows.
When walk in parallel system, the free leg should move back in line with the hip and not cross over the standing leg. Walking with a distorted line is the cause of instability, which is a common problem for beginners. When walking in cross system, you should rotate your hips before you outstretch your free leg, and the free leg must still move in line with the hip. You should not cross the free leg over the standing leg without rotating the hips. However, unlike in back ocho, the rotation of the hips does not need to be huge since you are just walking along the line of dance in cross system.
Tango walk is synchronous. The two partners walk not as two independent individuals but as a whole. Their legs must start, move and arrive together with exactly the same timing, speed and pace. It is important for the woman to constantly feel and mirror every inch of the man's movement and not land her foot too soon before he completes his step. A common problem is that she walks on her own and lands her foot on the floor before he finishes his step, causing him to step on her toes. The correct way is to hold her free leg outstretched in the air and allow him to push her, with the push of her own standing leg, so the two free legs may land on the floor at the same time and with the same pace.
Improving your walk is the key to improve your dance
One's walk defines one's tango, as demonstrated by my favorite tango couple Noelia Hurtado and Carlos Espinoza in the following dance. Pay attention to Noelia's walk and see how it relates to her dance. Walk is not only an important part of tango, but also the foundation of the dance because other steps are but variations of walk. For a woman, beautiful walk is a guaranteed eye catcher and proof of her ability. By learning to walk elegantly, your tango can be improved in more ways than you can imagine. (See Walk.)