Many people see a couple dancing smoothly together on the dance floor and imagine that the man is 'Leading' by pushing his body against the lady's in various directions, and she just 'Follows' with her body. But the truth is far from this simplistic perception. 'Following' is a very subtle and complex process, and can take years to perfect.
The big initial problem is that if you push most people: they start falling over. This is because the safest way to walk is not to push, but is to pull. We learn this by trial and error as infants. Initially the child stays balanced over their standing foot, and puts out their moving foot in the direction they intend to travel, then puts that foot down, and then pulls their body over it. This pulling method is a safe and secure method of travel with the body securely kept over one foot then the other during the process. Most people in due course learn to accommodate momentum and push initially with the standing foot while extending the moving foot forward, then continue the step by pulling with the forward foot. But most people never learn how to take a whole step while being off-balance.
When dancing, and a man starts to lead a lady into a step, he cannot just start putting a leg out in the direction of intended travel. That leg movement would be nearly imperceptible to the lady. He needs to lead with his whole body, and that will push the lady's body. That push will put her off-balance, but will also put him off-balance too. In learning to dance, they both need to know how to cope with being off-balance while taking a step.
The method of coping with this is for both partners to carry the moving leg directly under the body, just off the floor, while the step is being taken. At the end of the step, the moving leg is placed down on the floor, and the body will already be over it, and so will be balanced and ready for another step. The length of the step is controlled in this process by the push from the standing leg. There is no pulling. Unlike walking which involves pulling, dancing is all about pushing. During this pushing process, the body is, of course, off-balance. But by learning to keep the moving foot under the body, and putting the foot down at the end of the movement, the process is kept under control. Part of this involves defying gravity while off-balance. For a forward step: the weight of the body is ahead of the standing foot, and gravity will take the form of a 'couple' trying to rotate the body about the standing foot. To stop this creating a forward rotation culminating in falling flat onto the ground ahead, some very coordinated work must be done in the foot, ankle, knee and hip of the standing leg.
Before the movement starts, say for a forward step for the man with the left foot, and a corresponding backward step with the right foot for his lady partner, the man must move his body to transfer his weight to his right leg, and the lady must respond ('Follow') by moving her weight onto her left leg. Then the man must lower vertically into his standing (right) leg by coordinated bending of the right ankle, knee, and hip. The lady must 'Follow' this by simultaneously lowering vertically into her left leg. Simultaneously the moving (left) leg should be bent a little more than the right leg, lifting the right foot from the ground so that it can skim over the floor during the step. Then the movement itself, the 'step', consists of the man pushing his body: initially horizontally forward. Then as gravity starts pulling his body down, he must counter this by a coordinated and gradually increasing push upwards from his right foot, ankle, knee and hip, to keep his body moving along a horizontal line. Ideally only when he has a fully extended right ankle and knee, or he cannot keep from beginning to fall forwards, can he extend his left knee under his body, contacting the floor with his left foot to stand on it.
Meanwhile his lady partner is leaning gently forward against the man's body and so she can feel the horizontal flight of his body, and coordinate the muscles in her right foot, ankle, knee and hip, to match this body flight with her own body. But she now has an enormous advantage. She can let her standing leg extend forward as she moves away from it much more easily than the man can extend his standing leg backward as he moves forwards. The human hip allows the thigh to bend a maximum of about 20 degrees backward, whereas the hip allows over 90 degrees forward bending. She can keep her body flight horizontal more easily than the man can, and at the end of his step when he puts down his moving foot, she can sense this in his body, and so, just a moment later, put down her moving foot. Of course, this simple description is only the start of the couple learning to dance with each other. The 'step' they take together can be further enhanced by such developments as swinging the hips, and/or compressing even further at the beginning of the step to allow the man's lower leg to become nearer to horizontal with a bent knee at the end of the step, and/or the lady supporting the man against gravity towards the end of the step so that their body flight is extended. Men: if you think the above following technique is easy, then try practising with your partner in reverse roles, and let her do the leading. You will soon discover that 'Following' is not easy. Actually, she may learn that 'Leading' is non-trivial also.