Walking on your hands is a classic sign of elation, improves your upper body strength, and looks fun enough for you and anyone to try.

[edit] Steps

Choose a location with a soft flat surface such as grass or gym mats or have a spotter nearby.
Learn how to do a handstand (if you haven't already). It's essential that you master this step before moving on.
Get a trainer or a knowledgeable friend to spot you by standing a safe distance in front of you to catch and then hold your calves while you're in a handstand. They could also stand behind you, but you need to be careful not to kick them!
Put one foot in front of the other and raise your arms by your ears.
Lean over while swinging your arms out in front of you towards the ground. While you're doing this, start lifting your dominant leg behind you.
Push forward with your remaining leg and bring your hands to the ground, all while lifting your remaining leg off the ground. The trick is to do this all at the same time.
Put your legs straight up and balance yourself. Concentrate on keeping your legs in the air. You may have to stumble around on your hands to keep balance, but that's OK. If you have gotten this far, you can do a handstand. (Consult the Tips below for more on how to balance.)
Move one arm at a time while leaning slightly in the direction you want to go. Little steps are easiest if you are just learning.But after a while try taking bigger steps.

[edit] Tips

The main thing with balancing on your hands is to find your sweet spot, which means to center your body's weight as directly over your hands as possible. You'll get better at finding this spot with practice. Basically, you always have to feel as though you're barely not falling over (to the back). Don't be afraid to take that swing with your legs, because you'll probably never find your equilibrium otherwise.
If you feel your legs start tipping past your head, use you fingertips to push against the ground, as if you were trying to grab a large chunk of dirt. And if you feel your legs fall back down slightly, use the palm of you hand to move your weight onto your fingertips slightly ( DO NOT put all you weight onto your fingertips, this could cause you to break one or more fingers and potentially injure your back or spine )
Invest time learning 'Parkour' or 'Freerunning', this is a Paris-Born street art that teaches extreme balance and agility and takes no prior knowledge to learn.
One of the biggest parts to finding your balance is the way your legs are positioned. If you do a handstand and tip back to your stomach, you need to move your legs more over your head. However, if you move them too far over your head, you will tip over to your back. Upper body strength plays a role in that you can quickly readjust your hands to help you regain your balance.
Some people find that bending their legs when they're learning helps, and later you can learn to straighten them out.
If you are falling as though you are going to land on your back, you can always bend your arms, tuck your head, and roll out of the handstand. See the Related wikiHows below.
Prepare your arm, shoulder, abdominal, leg, and back muscles for this workout by exercising regularly. Don't expect that your body is going to be ready to do this overnight. Strength can compensate for a lack of balance and you need a certain amount of shoulder and trapezius strength to walk around comfortably. The nice thing with handwalking is that with practice, your body will naturally get stronger and you will gain better balance as well.
Tuck in your shirt!
Try practicing in a swimming pool to get the feeling first.
You could also try doing sit-ups or other core exercises to strengthen your abdominal and back muscles, because if you have a strong midsection, it will help you to keep your balance.
Keeping your toes pointed up helps you balance.
Keeping your stomach and butt tight will help with balance also.
Try doing handstands against a wall. It helps build the strength on your shoulders, which will also help with handstands.

[edit] Warnings

This will probably take you a long time to figure out. Don't be discouraged. It's going to take a lot of practice.
Stop when your arms are tired. As soon as you're getting dizzy, tired or frustrated, take a break! It's no use to keep trying under those circumstances, you'll learn nothing more. You aren't training anything by falling on your head.
The most prominent source of injury in this is falling on your back. Fall onto your legs if you can. An important thing to learn is how to roll out of a handstand. If you can do a dive roll, you should be able to roll out of a handstand.