Exercises
To learn the exercises and understand the basics, read the book Falun Gong, or "Chinese Falun Gong", the title may vary between editions. It has images of the exercise poses and explains their function in a technical sense. To get the movements right, you can watch the video linked in the OP. This is a follow-along instruction, with instructions in Chinese, so you should have read the book first, or you can't keep up. Once you know the exercises, you can use mp3s posted on the same website for the pacing and music.
Cultivation
The next step, after you know the 5 exercises, is to start on actual "cultivation". The introduction to this is a compendium titled "The Great Consummation Way", also linked in the OP. It's a ~50 page document explaining what cultivation is, and the function of the assistance center. It also explains how to set up your own assistance center. Anyone is free to do this with no contact with the organization in the USA. If people started actually doing this by this document now, independently, it may cause a revival of the original method.
Zhuan Falun
This is the main book of Falun Dafa. Notice the term here is Dafa and not Gong. That is because it refers to the "great law", Da Fa, rather than the "cultivated energy" which is called Gong. Falun Gong refers to the method of using the Fa Lun, "law wheel" to transform virtue, De 德, into Gong. Gong is "intelligent high density energy" and can manifest as supernormal abilities, such as those shown in Kung Fu movies. The term Gong is the same as Kung, those are just different spellings. Kung Fu of Gong Fu are "abilities gained from transformation of virtue".
To transform Virtue, De 德, you need to first have it. You will start with Ye 業, karma, and transform it into virtue. This is done by following the great law, Da Fa. The Falun Gong exercises only transform virtue into Gong, they don't create virtue from karma. This is a complex process taking place in everyday life, by following the law explain in Zhuan Falun.
For this reason, you need to read the book a lot, and understand how to apply its contents. This is called "Fa study" or "studying the law", and is a main activity, which is invisible to those who do not practice actively. If you haven't started for real, you will do the exercises and think this is all there is.