Introduction
China has long hosted  a variety of the most enduring religio-philosophical traditions of the world. Confucianism and Daoism, plus Buddhism, constitute the "three teachings", the cultural frameworks which historically have had a significant role in shaping Chinese culture. These three belief systems have been in constant (mostly harmonious) interaction and have often incorporated into the so called "Popular religion". To understand correctly Daoism, it has to be set in context with these other religious and cultural strands.

Relationship with other Chinese tradition: Confucianism
Confucianism is perhaps the most well-known of the textual traditions in China, developed from the teachings of the Chinese thinker Confucius. The Confucian texts became key to the orthodox state ideology of the Chinese dynasties, and although they were mastered only by a scholarly elite, they penetrated society deeply.
Confucius, whose Chinese name was Kong Qiu did not view himself as the founder of a school of thought, but he merely hoped to disseminate knowledge of wisdom and customs of ancient eras in order to restore his present condition that were in political and social turmoil.
Confucian teachings are not specifically religious, but are primarily concerned with the moral rules of conduct that all persons must follow, not because they are obliged to, but because, after having learned them through study and ritualized praxys, they know exactly how to behave in society. In the Confucian view  family and State are based on hierarchical relationships, which imply certain reciprocal duties, as well as the recognition of authority: the relationship between prince and minister, father and son, husband and wife, older and younger brother, older and younger friend. Human intercourse is governed by the values of Righteousness (yi), Benevolence (ren) and Filial Devotion (xiao), as well as the respect for the Rituals (li) that regulate the relations between human beings and between men, the State and the Gods (that is: the Imperial cult).
Through the interpretation of successive thinkers, Confucianism became strongly linked to the cosmic framework of traditional Chinese thought, as the Confucian ideals of ritual and social hierarchy came to be elaborated in terms of cosmic principles such as
Yin and Yang
Daoism and Confucianism.
The relation of Daoism to Confucianism has been complex. Confucianism focuses on the social aspects of human life. Also Daoism has interest in these issues, but its views are based on different grounds (see for ex. sec. 3 Excerpts from Daodejing). For this reason, the contrast between Daoism and Confucianism has primarily involved the social and religious sphere rather than their philosophical views.  In the eyes of the Confucian officers, the Daoist priests represented uncontrolled spiritual powers different from the official Imperial Cult. Replacing the state ceremonies with rituals addressed to the divine personifications of the Dao , performed by Daoist priests, would have granted Daoism an official role in the administration of the empire ( as often has effectively occurred). For this reason, the Confucians acknowledged Daoism only in its philosophical,or literary aspects, but regarded it under other respects as equivalent to common religion.

Relationship with other Chinese tradition: Buddhism
Buddhism is a religion that encompasses a variety of traditions, beliefs and practices throughout Asia, largely based on teachings attributed to Siddhartha Gautama ( also known with the epithet Shakyamuni, "the sage of the Shakya clan) who is commonly known as the Buddha. "Buddha" is a Sanskrit word meaning "the awakened one" . According to Buddhist tradition, Siddhartha Gautama, after a period of asceticism and meditations, "awakened" and discovered the Truth of the Things. and started preaching it. The fundamental doctrinal core of Buddhism, virtually common to any denomination, is a path towards the overcoming of suffering, caused by ignorance and craving, in order to obtain a blissful state, called Nirvana. Buddhism has played a central role in the spiritual, cultural, and social life of all Asia.
(see also Buddhism Module I)
Daoism and Buddhism.
Notwithstanding Buddhist polemical debates regarding doctrine and  political conflicts concerning the support by the imperial court, the relation between Daoism and Buddhism has been fertile, with reciprocal borrowings of doctrinal formulations, theological elements, technical terminology, and forms of practice and organization. Daoism provided Chinese Buddhism with some elements in the early stages of its development, and, in turn, drew from it in later times. The Buddhist contribution to Daoism is particularly noticeable in the developing conceptions of the afterlife. For the average person, anyway, Daoist or Buddhist deities could equally be addressed as needed and practicable, and subtle doctrinal distinctions surely were not the main concern.
Chan (Chinese pronunciation of Zen) Buddhism is thought to be born from early fruitful Buddhism-Daoism relationship.
(see also p. 7 of this Module and  Buddhism Module II, p. 3)

Relationship with other Chinese tradition:Popular religion
To define Chinese religion primarily in terms of Confucianism, Daoism, and Buddhism is to exclude from  consideration the ideas and practices that do not fit easily under any of the three labels. For the sake of simplicity, we can use the label "Popular Religion", provided that is just a superimposed category to a extremely broad and differentiated phenomena. Popular religion includes those aspects of religious life that are shared by most people, regardless of their affiliation. Three examples, all of which can be dated as early as the first century CE, could be 1) a typical Chinese funeral and memorial service, including the rites related to care of the spirit in the realm of the dead; 2) the New Year’s festival, which marks a passage not just in the life of the individual and the family, but in the yearly cycle of the cosmos; and 3) the ritual of consulting a spirit medium in the home or in a small temple to solve problems such as sickness in the family, possession by a ghost, or some other misfortune.
Daoism and Popular Religion.
The relation of Daoism to so-called Popular Religion is extremely complex. Briefly, Daoism has continuously integrated popular cults, beliefs, and practices. At the same time, the stated purpose of Daoism is to lead people to venerate the pure deities that impersonate the Dao, instead of joining cults defined as "vulgar". Within this context, the continuous incorporation of deities and ritual forms, resulting from the interaction of Daoism with local communities , had the purport of admitting the deities into the "correct" hierarchy of gods, and amending the ritual forms by integrating them into the proper way of communicating with the divine and spiritual world.
(See also p. 5)

Source Analysis

Source n° 1
The three teachings
In this work, Confucius approaches from the right, greets Shakyamuni, lifting his united hand under the robe. Shakyamuni wears a red robe and can be easily identified by a cranial protuberance symbolizing wisdom. Holding a roll of his Daodejing , Laozi stands behind Shakyamuni.
As early as the Tang dynasty (7th- 10th cen.), there are traces of the syncretism of the “Three teachings” , which became a popular movement in Song (10th-13th cen.) and Ming China (14th-17th cen). It was a mixture of Confucian ethics, the Daoist practices and the Buddhist concept of reincarnation. Confucianism provided ethical guidelines for maintaining social order. Daoism offered mystical ideas about one’s health, well-being, and longevity, while Buddhism dealt mainly with the afterlife, the effects of good and bad Karman and promised release from suffering. The school of the “Three teachings” was rejected by most Confucians and Buddhists but received wide support in Daoist circles, such as the Complete Perfection Schools (see p. 7).
The depiction of the three founders in such harmony conveys a thought prevalent during the mid-Ming period, when this painting was created.

Source n° 2
Excerpts from the Confucious's Analects
Glossary:
In the first excerpts is explained how Filial devotion (xiao) is the pivotal value for a harmonious society, for there is less probability that a faithful son or brother to develop behaviors that ultimately will lead society into disorder. Moreover, as stated in excerpts n° 2, Filial devotion and other righteous attitudes must not be imposed by law and under the threat of punishment, but should be cultivated and nurtured autonomously through the repetitions of Rituals (li), such as ancestors worship, imperial cult and so on.

Source n° 3
Tossing of the "Ghost Money"
Ancestor worship is a strong tenet in most forms of Chinese religion and usually includes the offering of sacrifices and gifts to deceased relatives. "Ghost money" Known also as ‘joss  paper’,  is one such gift. "Ghost money" can be any of several types of fake currency that are burned as a sacrifice to deceased ancestors. These money will help economically the ancestors in their afterlife. The burning of ghost money is also very common practice at Buddhist and Daoist temples.

Intercultural and interdisciplinary information
(History)
A good point for starting a comparative discussion is the coexistence of Judaism, Christianity and Islam in Medieval Spain. See also the dedicated Digital Module.

Link to other Modules
Module: "The three monotheistic traditions in medieval Spain and Sicily. "
Buddhism Module II, sec. 3