In tango training, there's a lot of emphasis placed on axis, embrace, posture, elegance, and a whole host of other concepts that can overwhelm and overshadow a very simple point:
If your base is not under control, then everything above it will follow. Establishing a clear understanding of how you connect to the floor underneath you will lead to better dancing through a better understanding of your own balance and how your body is poised over your foot.
Either barefoot or wearing socks, stand with feet parallel (the outer edges of each foot placed parallel to each other). Try and evenly distribute your weight across the soles of both feet, keeping a gentle bend in the knees and ensuring that your knees track over the second toe of each foot. You can imagine the feet as forming a square, with the ball of each foot forming two corners and the heels the remaining two. Take a few seconds to feel how your body is positioned over your feet in this position.
Then begin shifting the weight entirely between both feet, being sure to continue to evenly distribute the weight across the whole surface of the foot. Recenter your weight.
Begin the process again, but this time rocking back and forth from front to back while keeping your weight evenly distributed between both feet. Test the comfortable range of your balance- there's no partner to throw off, so really push to where you are tottering on your heels or hanging on by your toes. Take note of the different compensations you make to maintain your balance at the edge of your balance. Recenter your weight in the center of your square.
Finally, shift your weight forward off of your heels, alternating right and left. At this point you should only be utilizing one corner of your square at any time. Test how long you can continue shifting without replacing your heels on the floor.
At any point, feel free to take a quick walk and shake your feet out- and that's it! This is the first of what I hope to be many small exercises that can help you improve your dancing.