How to do … HSPU
What it is
You go into a handstand leaning on the wall. Lower your body until your head touches the floor (or mat, ab mat, towel ... just the floor might be quite hard). From here, press yourself up until your arms are fully locked out. Your heels must have contact with the wall in the end position (there is btw also a free handstand push up without wall support or even one in the rings, but let's stick to this basic movement in CrossFit).
Where the problem lies
Shoulders! The HSPU is a pretty much isolating movement challenging mostly the shoulder and triceps. Of course, there is some core and chest involved in every press, but a decent strength in your delts is a must.
Especially the strict HSPU can be compared with a strict press. But no worries, the range of motion is a lot shorter (it's like starting the press with the barbell on eye level), so you don't need to strict press your own body weight to master it. But a 1Rm around 85% BW should have been achieved.
The kipping HSPU requires even less strength since you can help with a kick up of your legs. Still you need explosive power, a fast body extension and a good timing.
How to practice
For many CrossFit beginner, going into an upside down position is scaring enough. Start with wall walks: Walk up the wall facing the room, until your chest touches the wall behind. This is already the handstand position - you know now that your shoulders and arms have the strength to carry you.
For the first kicks into the handstand, it might be helpful to have someone spotting you. I also find it easier to start from a standing position and then just swing my hands down to the floor and swinging my legs up in one fluent motion, almost simultaneous, than starting with my hands on the ground.
If you can't do a strict HSPU yet, shorten the ROM by using two ab mats or put a plate under the mat. Anyway, it doesn't make sense to use more then 2 mats since the range of motion gets too short in the end - better do push ups in that case, with your feet on a high box.
Another hint for the strict one: Don't rest in the bottom position, especially when using an ab mat. Don't let your head sink in too deeply and loose all your tension. "Bouncing" the reps out makes it much easier.
The kipping is a quite personal thing. Some people prefer to pull their knees all the way down to the chest while others only tuck them in a tiny bit. I prefer to start with my legs open (knees apart from each other) and close them on the way up in the extension. However, the leg extension must be as fast, explosive as possible to generate a momentum that let your body fly up!
For both versions: Don't place your hands to narrow to each other. Having decent space in between is another reserve to shorten the way you have to go.