The Yang-style 24-step Tai Chi routine is the most widely practiced form in the world. It is said to be simplified in the sense that it is short—much shorter than the traditional Yang-style long form on which it is based—and some movements have been modified to make them a little easier for beginners to learn. Here is a brilliant demonstration of 24 by Gao Jiamin:
The name of the form is 二十四式简化太极拳 (Èr Shí Sì Shì Jiǎnhuà Tàijíquán): 24-style Simplified Tai Chi. Here is a PDF list of the 24 movements.
Many people practice this form with little or no training, and it’s the only Tai Chi they know. Others learn 24 as an introduction to Tai Chi, train to a higher level of performance, and then move on to learn longer and more advanced forms.
Among this latter group, many continue practicing 24 routinely as a review of fundamentals. Twenty-four may be simplified, but it’s not easy! With heel kicks and xiashi duli (low form to standing on one leg) on both sides, it is as physically challenging as Yang Tai Chi gets.
History of the form
Twenty-four dates from the 1950s. At that time, the prevailing Tai Chi practice was the long form of Yang Chengfu. That form is a brilliant exercise, but it is very long—85 to 108 moves, depending how you count it. The problem is not so much that it takes a long time to perform (25-30 minutes) but that it takes such a very long time to learn. Most people never get there.
Recognizing that tai chi was a remarkably good exercise for health and longevity, the Chinese government’s sports commission sponsored the development of a shorter, more accessible form for beginners, in hopes that more people would learn and practice tai chi.
Yang Chengfu was long gone, having died in 1936. A number of well-known masters were consulted or involved in this development project. Li Tianji—son of Li Yulin—was a leading creative force behind the new form, and it was Li who wrote and illustrated Simplified Taijiquan, the first textbook on 24, which was eventually distributed to physical education departments throughout China.
In any case, the resulting form has only 24 movements derived from the traditional long form and little or no repetition. The long form contains 50-odd unique movements, so 24 has not quite half as many moves. It can be learned in a matter of weeks or months, not years. A person who has learned 24 can then move up to the 108 fairly quickly, having already learned the fundamentals of Yang-style Tai Chi and nearly half of the moves in the long form.
Instructions
Instructional material for 24 abounds. Arguably the most authoritative is this instructional video by Li Deyin, nephew of Li Tianji and for many years one of China’s most influential teachers, as well as its number one tournament judge. He has produced a number of instructional videos on 24. This one is almost two hours long, very complete.
This video is in Chinese. Li does a lot of talking, but if you are patient, you can learn from watching. He’s very clear, shows everything from multiple angles, and goes into great detail. After a brief introduction, a full demo starts at 3:15, back view of the first part at 9:00, and instruction begins at about 17:00.

Professor Li’s book, Taijiquan, is a useful reference for 24 (and a number of other forms). The chapter on 24 is written by Li Tianji himself and illustrated by photographs of him demonstrating the movements. https://www.amazon.com/Taijiquan-complimentary-DVD-Li-Deyin/dp/7119037080/
How 24 is different
Although the 24 moves are derived from the 108, they are not all exactly the same. In fact, 24 is revolutionary in some respects. For one thing, the traditional forms tend to be one-sided; a lot of moves are only ever practiced on one side.
Twenty-four, by contrast, is more left-right balanced. Grasp the Bird’s Tail is practiced on both sides in 24, and Snake Creeps Down is performed on both sides as well, which makes the Golden Rooster Standing on Right Leg considerably more difficult than it is in the 108. This left-right balance turned out to be a trend; nowadays, in contemporary forms, we practice almost everything on both sides.
The retreating move in 24 is simpler than the traditional Repulse Monkeys. Some people call the backward-stepping move in 24 Repulse Monkeys, but it is a different move and has a different name in Chinese. Repulse Monkeys is 倒攆猴 Dào niǎn hóu, and the move in 24 is 倒卷肱 Dào juǎn gōng (Go back whirling forearms).
The upper body movement in these two steps is pretty much the same, but the footwork is different. Many beginners have a hard time learning the footwork for Repulse Monkeys. Dao Juan Gong is a more basic 退步 tuìbù (step back)—step straight back, from empty stance on one side to empty stance on the other.
In practice
I love 24 and practice regularly to keep my fundamentals up to speed. My only comment would be that 24 requires a warm-up. The 108 starts so gradually that by the time you get to the more demanding moves, you are ready for them. When you do 24, you are doing heel kicks and squats within two minutes. Of course, you could take it easy, but I like to practice 24 after I am thoroughly warm so I can perform each move as well as I can. Ba Duan Jin (the Eight Brocades) serves very well as a warm-up for 24.
My backyard 24 below is considerably less impressive than the world-class performance by Gao Jiamin above. This is more like what most of us do: