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 men lead women in tango, it's women who beautify 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 clip.
When done in slow motion, this exercise can effectively build foot muscles and improve stability and elegance in women's walk. The exercise can be summed up in six steps to help you memorize the sequence: (1) Stand on one leg and stretch the other leg forward. (2) Transfer the weight forward until you stand on the heel of the front foot and the toes of the back foot. (3) Change weight back and forth a few times in that position. (4) Transfer the weight to the front leg completely. (5) Start the next step by swiveling the hips and using the hip to move the leg - this will give women's walk a feminine look. (6) Repeat the sequence with the other leg.
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 clip, 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. Women using open hand holds in the dance cannot stretch their 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 clip by Jennifer Bratt and Ney Melo.
Notice that Jennifer leans on Ney with an increased gradient. She bends her standing leg and uses a little bit dissociation - turning her hips slightly upwards and downwards to allow the leg to reach back farther. Notice also that when her hips are turned, she uses the thumb rather than the toes of the foot to reach the floor. Also notice that her leg is swayed by the hip a little bit sideways in contrast to the forward walk in which the leg is swayed by the hip towards the center, as demonstrated by Vanessa Gauch in the first clip. All these add a feminine touch to her walk.
Good tangueras all use the hip to move the leg, without exception. Here is another excellent example, danced by Mariana Montes with Sebastian Arce.
Their style is too exhibitionist to suit the milonga, especially on the leader's part, in my humble opinion, but the opening walk (0:15 - 0:28) is absolutely gorgeous, appropriate in social dancing, and worth watching again and again. The walk is done in close embrace that enables Mariana to stretch her leg out farther. Her beautiful hip sway, combined with a subtle dissociation and a very straight leg line, all contribute to the unequivocal beauty and elegance of her walk. Notice that her leg is also swayed slightly sideways as a result of using the hip to move the leg.
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 the 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 straight knees
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 the free leg is completed. In order to do that you should not use the leg muscle to move the free leg, which is the cause of the curve of the leg. Rather, you should lift the hip and use the hip to swing the leg so the leg remains straight, and you should not bend your free leg when transfer weight to it, but keep the leg straight until it carries 100% of your body weight. Keeping the knees straight can make your dance look more elegant, as this clip shows.
When walk in parallel system, the free leg should move back on its own line, that is, be aligned with the hip, and not step over the line to cross 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 swivel your hips before moving your free leg in-line with the hip. Crossing the free leg over the standing leg without rotating the hips is a common problem for beginners. The hip rotation, although adds a feminine touch to your walk, does not need to be huge since you are just walking along the line of dance in cross system.