After a long period of getting used to the invert position (see Wall Headstands) and gaining enough balance (see Crow Stands) and strength (see Wall Handstands) to master handling your whole bodyweight on your arms only, it's finally time to start with the actual exercise - The Handstand Push Up. To begin with hspu I advise you to do Half Handstand Push Ups first, as you will still need to add more power to your shoulder muscles to perform the full range-of-motion of the exercise. I can tell you from my own experience with this exercise that it's a real feats of strength and bearly seen in a gym, so it might be possible that you get some attention from other gym members who are confused to see you doing this. Most people train their shoulders with press exercises, where you lift a weight (dumbbell, barbell, kettlebell) over your head, but there are few people who are able to press weights equivalent to their own bodyweight, which is actually what you do by performing hspu (and you gained the strength for starting with it through the preliminary exercises). By practicing half hspu your upper body strength and your balance will continue to increase rapidly and this will make a huge difference in appearence, strength for other exercises and health of your muscles, joints and tendons at your arms, neck and shoulders. It's vitally important that you don't overestimate yourself by doing hspu. If you feel that you aren't ready for them, do the previous steps for one more month to get a safer feeling. If you feel that your muscles get tired during the exercise stop immediately, because muscle failure could be dangerous as you are upside down and I guess you don't want to crash on the floor with your face first. You don't have to start with a big range of motion, just do a small one in the beginning and increase it from session to session.
Let's start with the how-to-perform explanation:
The first part is similar to normal wall handstands: At first you have to find a solid wall or tree stem (you can use the same as you already used for wall headstands). Get down on all fours and place your palms about shoulder-width apart on the floor (approx. 6-10 inches from the wall). Your arms should be extended. Now bring the knee of your stronger leg close to your corresponding elbow and straighten out the weaker leg. Push down with the strong leg and kick the other leg simultaneously in the air. Both legs should now move up in the direction of the wall. After your feet touched the wall, straighten your legs until your body is aligned. Breathe easy through your nose. The contact with the wall should be with your heels only (the body is slightly curved in the pose).
Now comes the actual push part: Just bend slowly at the shoulders and elbows until your head is halfway towards the ground. Pause for a second and push yourself up slowly to the start position. Repeat the movement as often as possible (up to the requested amount). If you can't manage to hit the target instantly just do 2 sets of as many reps as possible and try to add a rep every session until you are able to manage the target reps. As it may happen that you get problems with your shoes "sticking" to the wall (depending on the surface of the wall) you have two options to avoid this. Firstly, at some surfaces it could help to do the exercises with socks only (they "slip" better along some walls as shoes do) or, secondly, you try to get a bit off the wall with your feet during the push part (as it would be, if done without the support of a wall).
Target: 2 sets of 20 reps
When you don't feel ready for handstand push ups yet, but the wall handstand already became an easy exercise for you, you may have the feeling of doing a step in between those exercises. If this is the case, you can do Inverted Shoulder Presses to gain more strength in your upper body. I also add this exercise after performing half hspu to squeeze the last power out of my shoulders and triceps (it's not as risky as hspu are when your muscles are already tired).
As I'm just writing an article for my blog and not a whole book about hspu, I won't describe the whole exercise but show it to you in a video. Just take care about a straight back and do 10-20 reps per set.
Last to say: I really love doing handstand push ups and I bet you will as well!