One of my favorite simple movement practices that can be done almost anywhere at all is shifting forward and back. Starting with your feet about shoulder-width apart, move one foot forward anywhere between a few inches and a whole foot. This exercise actually works best if the stance isn’t too wide, so I usually keep my foot closer than if I was actually walking.
From this position, begin slowly shifting the weight to the front foot and then to the back foot. When I say slowly, I don’t mean just moving slowly, though, there has to be stability present in both feet all the time. You should be able to pause at any point during your shift and be totally comfortable. Another way to look at this is that if someone were to come push on you, you wouldn’t immediately topple over.
The key to this stability begins in the feet. Keep both of your feet flat on the floor. Notice where your weight moves along the bottom of your feet, sometimes alighting on the balls, sometimes the heels, sometimes one edge or the other. The foot is designed to spread weight out like an arch, across the whole foot and down into the ground below. When you feel more weight in the ball of the foot, then a shove from behind will uproot you more easily, so try to keep the weight evenly balanced between ball and heel.
As you shift, it’s common to throw your hips forward and allow your legs to handle it. In this exercise, move with your legs the entire time. When you shift forward, push with the rear leg, when you shift back, engage the front leg. This will also keep you connected and stable on the unweighted leg, which in turn will improve your overall stability tenfold.
Once you’re comfortable with this practice, try it with your eyes closed, swapping forward and back leg every so often. Feel and try to relax any tension in your body and allow the legs to control the movement. Your body can learn a lot from just this.