When it comes to holding a handstand, there are many factors to consider. Here you can see the most important ones explained by a very skilled guy named Chris Silcox.
To start practicing, do a handstand against the wall and slowly take one leg off at a time while finding a balance. When you find your “sweet spot”, pay particular attention to your fingers which pretty much act as feet while you are upside down. Much like toes, fingers are engaging and releasing in order to keep us in balance. Another good tip is to learn to manipulate your shoulders and elbows to prevent going off balance.
You may also want to start the other way around, with your face facing the wall without arching your back. Try to get your fingers as close as possible to the wall and start balancing. Go for one leg at a time like before and make sure to use your fingers to prevent falling to the other side. You can also move your shoulders to the wall to avoid the same problem. If you don’t have a spotter, the best way to come out of this position is to walk your feet down slowly.
P.S. Check out Hand Balancing Made Easy for all information you’ll need to learn how to balance on your hands.