The Tao

Philosophical Taoism (Daojia)
'The Tao' is in Daojia the ultimate reality. Tao is the principle for all existence and a force that guides life, balance and change. The Yin-Yang symbol, or the Taijitu, shows how the Tao works as complimentary opposites and how they're dependent on each other. Yin can't exist without Yang, after rest comes action and after action comes rest. The teardrop shapes signify movement and cycle, while the dots in each halve represent that nothing is purely Yin nor Yang, e.g. empathy hidden in hate or sadness in joy.
Meaning
Yin is the black side and represents negativity and passiveness where Yang represents positivity and activity. Yin, at its core is about cold, darkness and being receptive. Yang is warm, bright and active. Originally, Yin and Yang were not tied to gender roles. Confucianism later reinforced and tied certain traits from Yin and Yang respectively to certain genders, e.g. logical for Yang, so that goes to men. Yin is nourishing, so that goes to women. Taoism itself doesn't teach gender roles and says that there's both Yin and Yang in every person.
Wu Wei
Wu Wei is generally translated as 'actionless action'. Essentially, it's where you're in perfect harmony with the flow of the Tao. Wu Wei is about efficiently doing you need to do without unnecessary struggle or force. Instead of control, Wu Wei is aligning with the natural order instead of forcing an outcome. Think of it like growing tree. It doesn't grow by force, but rather because of the will of nature.
Ziran
Ziran translates to "of its own; by itself". The general gist is that one should act without overthinking, something that happens without much force in conscious life. You don't think, you do.
Mastery of an Art
You're in harmony with the Tao when you've mastered a skill. Because you've trained for it, yes, but it's more about aligning yourself with the task. A writer can try his best to come up with a story, but a writer with Wu Wei lets the words come to him.
Egoless
To achieve Wu Wei, one must let go of obsessing over outcomes and their ego. With excessive willpower comes resistance, think of it as a dictator suppressing their subjects. Water, which slowly wears away a stone given enough time, experiences no resistance. Keep in mind that the desire to becole egoless can in itself become ego-driven. Wu Wei = not clinging onto achieving it.
Religious Taoism (Daojiao)

Note: This is a summary, don't take my word for it!
In Daojiao, the Tao is a divine energy that you can harness through meditation, various rituals and magic (alchemy). The Three Pure Ones are the manifestations of the Tao. (Religious) Taoists attempt to merge with the Tao for immortality. Two types of methods are used to achieve Xian (immortality), those being Inner and Outer Alchemy.
Inner Alchemy
This practice consists out of three treasures (Jing, Qi & Shen). First, you have Jing which is essence. One can preserve this by resisting their urges and preserving more Jing.Qi
This allows for the creation of higher Qi (energy) which travels by reserve breathing (inhaling with mouth and exhaling with nose) up to your lower abdomen. Next, you need to transform that Qi into purified consciousness (Shen).
Shen
Do this by meditation. Lastly, refine your Shen into Void, i.e. opening your third eye. Breathe as stil as an embryo, thus returning to your pre-birth state. Note that this is a lifelong path and rarely achieved in a single lifetime.
Outer Alchemy
Achieved through consuming elixirs which often contained gold, cinnabar or mushrooms. Note that this method is not widespread (anymore) as many Daoists historically died from mercury poisoning after attempting to purify their body. Inner Alchemy, which is more metaphorial, is the more common way.