Hi,
Try this. From your standing position with both feet on the floor.
1) 'Shift' your weight over the foot that will be supporting you. When you do this, you are establishing a 'centerline'. This centerline goes through your foot into the ground, and up through your crown. Find this centerline, feel your connection to the earth (grounding). I grab the ground a bit with my toes/foot. You feel an increase in weight over this foot that will support you.
2) Draw your free foot across the floor to the other foot , 'before' you pick it up, so you are bringing it to that centerline. Don't pick it up from where it is.
3)Bring that free foot over to the other one, then, pick it up. It is almost like going 'up' a fire pole.

You have to establish your centerline, before you pick up your foot. You will be off balance, immediately, if you don't. Shifting your weight, first, finding that centerline, aligning through your feet and crown, bringing the free foot 'to' that centerline, and going straight up this newly established centerline. You establish your centerline, before you pick up the foot.
If you are standing on both legs, centered, and pick up one foot, you will fall down. Without the 'shift' to a new centerline, you are off balance as soon as you pick up the foot. There is a nice singular vertical alignment in this. Keep aware of the foot supporting you. Don't stand on top of the ground. Your weight is sunk, through it. You don't go lower, you just keep your knees bent the same. Keep this sense of sinking, or a consistent centeredness, or head at the same level, and don't raise everything up as you lift your knee. Only that free leg moves and lifts. Everything else, concerning your stance, is very firm , centered, grounded, etc.. It is a very stable position, that you have, as you raise that leg. Focus.
Standing on one leg is a basic. It is great for increasing your sense of grounding, when you lower to standing on both feet. Try it sometime. Just going from both feet, to picking up one foot, wait a bit, then put it down again, and feel your connection to the earth again with both feet. It strengthens your stance and sense of grounding. Like one can take for granted, having both feet on the ground!
love,
gallen