The press to handstand is a fairly general name, that commonly refers to any straight arm press. This is different from the many bent arm presses, which are still presses up to a handstand, but are usually called something different.
Among the straight arm variations, the most common and easiest to begin with is the straddle press, where the legs are spread wide.
There is also the pike press, which is harder to do, because having the legs together increases the leverage.
Here is a good video tutorial on the subject
1) Straddle Lift off the Floor Holds
2) Straddle Lift Pressup
3) Straddle and Pike Stretch
4) Trying the Press to Handstand and Lifting Toes
5) Straddle Press Against the Wall
6) Straddle Press with Feet Raised to Start
I would partially disagree with her statement to never jump. While that doesn’t qualify for the full skill, you can use a little hop in training for this exercise.
Also the floor press handstand (where the legs start on the floor) is a harder skill then just pressing with your feet starting on the ground.
Be forewarned this exercise can be very difficult to do, especially for men. The biggest thing likely to hold you back is flexibility, more so then strength. Much work needs to be done on these drills and others to attain this skill. In addition to the hamstring and hip flexibility you need lots of compression ability, that is compacting your upper and lower body together.
I’m personally still working on this skill as it’s long eluded me, but I am getting ever closer.
There are many more advanced variations of pressing to handstand, like from an Lsit or even on one arm as is seen in the video below.