You have a center point and a center line. The center point drops and rests on the ground and from there moves, expands, shrinks. Become more aware and able to achieve this activity of sinking to build a sense of alignment. From feet to top of head, you can see it as the middle line up and down in the spine. The bubbling well, or bubbling spring (yongquan), is key in helping you feel for it.
What throws you off balance when you stand on one leg is the tensing of the muscles in the soles of the feet, the ankles and calf muscles are thrown out of balance when that happens and you fall. It is crucial to become aware of what the muscles in the feet are doing. You want them to stay calm and not clench.
Moving from the feet. Initiating movement from the soles of the feet in such a way as to allow the rest of the body to follow. The body becomes and remains a single cohesive unit while in the midst of moving. Each part adjusts according to the message sent to it by adjacent parts, or even the point of initiation. Much of that adjustment is a letting go of tension in those very same parts. Letting go allows qi to flow and circulate through the body, thus providing greater benefits.