Introduction
Even if it is impossible to define one authentic and  coherent “traditional Chinese worldview”, there were still some basic principles concerning human existence and the functioning of the universe that somehow informed all the varieties of religious trends in traditional China. The concepts most relevant in Daoism are  the idea of Qi, the Yin-Yang cosmology, and the Five Agents. In Daoism, this dynamic worldview serves not only to explicate the functioning of the cosmos, but also to illustrate the view that all  phenomena ultimately originate from the Dao, and that the different forms of the world are contained within Its principle. At the same time, this correlative cosmology serves to regulate the religious modality of approaching the Dao

Main doctrinal tenets: The idea of Qi
The basic stuff out of which all things are made is called Qi. Everything, at its fundamental level, is made of Qi, including inanimate matter, humans and animals, the sky, ideas and emotions, demons and ghosts. As an axiomatic concept with a wide range of meaning, the word Qi has over the years been translated in numerous ways: psychophysical stuff,"pneuma" or vital energy. For Daoist, the first emanation of the Dao is called the Primordial Qi, which differentiate itself in Yin and Yang.

Main doctrinal tenets: Yin-yang complementary cosmology
In Chinese cosmology, Yin and Yang are two opposite but complementary principles that regulate the functioning of the cosmos. As the two aspects of the Dao, their continuous alternation is at the origin of the rise and disappearance of all phenomena. Probably, Yin and Yang originally denoted the shaded and sunny sides of a hill. Later on they began to be used as cosmological principles, probably following this kind of reasoning: since the sun has not yet warmed the Yin side, it is dark, cool, and moist; plants are dormant and water in the form of dew moves downward. The Yang side of the mountain, on the contrary, it is bright, warm, and dry; plants open up and water in the form of fog moves upward. This basic symbolism was extended to include various other pairs:  heaven and earth; above and below; day and night; summer and winter; spring and autumn; man and woman; active and passive, and so on.
Between the third and the second centuries BCE, the notion of Yin and Yang became one of the pillars of the Chinese cosmology.  Yin-yang theory sometimes placed these pairs on an equal level, considering Yin-Yang alternating, complementary principles, relative to each other. Sometimes, on the contrary,  Yin-yang theory ranked them hierarchically, putting greater value on the active and masculine Yang side. Daoism chose the balanced and harmonious view of the relationship.

Main doctrinal tenets: Five Agents and correlative thinking
The Five Agents theory added further nuances to the Yin Yang cosmology. The Five Agents  symbolizes the modality in which the Dao differentiate itself, represented by Wood, Fire, Soil, Metal, and Water. These are to be seen much more like phases of a process of change, rather than mere "elements". As Yin constantly become Yang and vice versa, so Wood became Fire, that became Soil, that became Metal and so on (see below analysis of source n°3).
Moreover, directions of space, seasons, colors, planets, organs, family relationship and so forth can be assigned to one of these emblematic categories in order to define not only the relations that occur among the elements of a series, but also those that occur among the different domains. Wood, for instance, is associated with the east, spring, the color green (or blue), Jupiter and the liver. The purpose of correlative cosmology, therefore, is not to explain what causes an entity to exist or a phenomenon to occur, but to define its relation to other entities and phenomena. An important corollary to this view is that cosmos, deities, human being, society, ritual area and so on are analogically related to each other, so that an event or an action that occurs within any of these domains can be relevant for the others.

Analysis of Sources

Source n° 1
The Taiji diagram
The Yin Yang symbol (better said Taiji diagram) must be viewed as a dynamic symbol in circular motion: when one of the two principles prevails, the other surrenders, but once one of them has reached the peak of its development, it begins to recede — and in that very moment, the other principle begins its growth. This mode of operation is especially visible in the time cycles of the day (alternation of daytime and nighttime) and of the year (alternation of the four seasons).

Source n° 2
The Chinese character for Qi
Etymologically speaking, the character depicts  气 (“steam”) over  米 (“rice”); Qi is analogous to steam produced from the cooking of rice. In the context of traditional Chinese and Daoist cosmology, Qi is viewed as a subtle vapor that animates every sentient being and that circulates within and between all that exists.

Source n° 3
There are two patterns of dynamic interaction between the Five Agents and their various associations. The first is called "pattern of creation":
Wood feeds Fire
Fire creates Soil (ash)
Soil bears Metal
Metal enriches Water (as in water with minerals is more beneficial to the body than pure water)
Water nourishes Wood

The second is the "pattern of control":
Wood grapples Soil (with the roots)
Soil dams (or muddles or absorbs) Water
Water extinguishes Fire
Fire melts Metal
Metal chops Wood

Intercultural, interdisciplinary information
(Philosophy)
The most famous Western thinker usually compared with the Chinese idea of reality in constant flux is  Heraclitus of Ephesus (c. 535 – c. 475 BCE). For more information about Heraclitus and Daoist thought see: http://punzel.org/Ephemeris2013/Butti.pdf.
Moreover, Many philosophies and worldviews have a set of classical elements believed to reflect the simplest essential parts and principles. The ancient Greek belief in five basic elements, (earth, water, air , fire  and aether), dates from pre-Socratic times and persisted throughout the Middle Ages and into the Renaissance, deeply influencing European thought and culture (see also intercultural information in p. 4). However, the Chinese counterpart were understood as different types of energy in a state of constant interaction and in flux with one another, rather than the Western notion of different kinds of material.