You will need to have the strength to hold yourself upside down. Push-ups, bench press, strict press, dumbbell and barbell rows will all help you gain that strength. A close grip form will best transfer over to the handstand (which is what we are trying to do). Keep your arms and elbows close to your sides. We want to work your triceps, back and shoulders. The narrower the better. You are doing these movements to gain strength. Stick to the most challenging version or heavier weights for small sets.
Then you'll need to get comfortable being upside-down. Practice a good static handstand. Hands go to the floor with arms locked out. Kick up to the wall keeping legs together and pushing up out of your shoulders, making yourself as tall as possible. Look behind you.
Once you have a reliable handstand you can begin practicing the push-up piece. This is an upside-down strict press. So while it is tempting to look down at your hands, think about how silly it would be if you looked up at the ceiling while pressing a barbell. Begin by lowering your body to a pillow or several pillows. Keep working on the strength pieces and with time you will get the full movement.
Notice how I didn't explain the kipping handstand push-up? I believe that like the pull-up, it is safer and most beneficial to the athlete to be able to do the strict version before attempting the kipping.
If you are looking for a specific routine please reach out to me and we'll see what we can come up with.