Here is the answer in brief:
Buddhism is the following of the words of Buddha.
Zen is a form or method of Buddhism and follows the same basic principles of Buddhism.
Taoism is both a philosophy and a religion:
– The Philosophical Taoism focuses on the unity of the universe and all things being united in the Tao. Tao translates as ‘way’ and is the name given to the underlying presence of the universe even though it is unnamable.
– Religious Taoism expands on the philosophical teachings and adds deities, mysticism and folk religion elements.
For greater detail, read the entire post.
First, Zen IS Buddhism. Zen is a form of Mahayana Buddhism. In China it is called Ch’an, in Korea it is called Seon, in Sanskrit it is called Dhy?na. It started in India and moved to China, Korea, Japan and many other South East Asian locations and eventually into the United States and the rest of the world. The basic teachings are the same in Zen as they are in all forms of Buddhism. The biggest difference between Zen style Buddhism and other sects of Buddhism is the emphases on meditation over the reading and chanting of Sutras. (This is not to say that they do not study sutras, but it is not as important as understanding the Buddha nature already within us.)
The basic teachings of Buddhism are simple:
I) The Four Noble Truths:
1) There is suffering and impermanence in life for all beings.
2) There is a cause for suffering, which is attachment, desire and ego.
3) There is a way to stop suffering, which is to eliminate attachment, desire and ego.
4) There is a path that leads out suffering called the Noble Eightfold Path.
II) The Noble Eightfold Path:
1) Right Understanding – knowledge with regard to the origination and ending of suffering
2) Right Thought – Being resolved on renunciation, on freedom from ill will and on harmlessness.
3) Right Speech – Abstaining from false, divisive, abusive and idle speech.
4) Right Action – Abstaining from stealing, improper sexual activities, and actions that cause others to suffer.
5) Right Livelihood – Abandoning any livelihood that goes against the dharma.
6) Right Effort – Upholds and exerts intent for the sake of Dharma.
7) Right Mindfulness – Remaining focused on (ardent, aware, and mindful) of the self, the mind, and the body (Removing ego, putting away greed and removing distress.)
Right Concentration – Being mindful and alert of all things.
III) Taking Refuge in The Three Jewels:
1) The Buddha
2) The Dharma (The teachings of the Buddha)
3) The Sangha (The community of people practicing the Dharma)
IV) The Five Precepts
1) To refrain from harming living creatures. (Physically. Mentally, Emotionally)
2) To refrain from taking that which is not freely given.
3) To refrain from sexual misconduct. (Conduct that causes physically. Mentally or emotionally harm to others or ourselves)
4) To refrain from incorrect speech (lying, harsh, hurtful language and idle speech.)
5) To refrain from intoxicants which lead to loss of mindfulness.
V) The Unborn or Buddha-mind: Understanding, realizing and living in our unborn Buddha mind that we all possess.
Taoism is both a philosophy and a religion. The philosophical aspects of Taoism revolve around the idea of Tao. Tao translated as ‘Way’. The way is unnamable and indescribable but it binds all living things together. For this reason, Chinese Ch’an and therefore Zen, has incorporated the philosophical aspects of Taoism into the religion of Buddhism. In fact, some Ch’an temples teach lessons on the Tao Te Ching just as they do Buddhist Scriptures. Once both philosophical Taoism and Buddhism are studied, the similarities are obvious. For instance, Buddha taught that his teachings could not bring about enlightenment; he could only point the way. Likewise, Taoism teaches that the way of the Tao can not be found in a book or in a classroom, these things can only be used to point to the true way of the Tao. As this illustrates, the two work well together.
The religion of Taoism, can be broken down into two main groups:
I) Organized Chinese religious movements such as Zhengyi and Quanzhen that collectively trace their roots back to Zhang Daoling in the late Han dynasty. The fundamental beliefs revolve around:
1) The wisdom of the Tao
2) The Five Elements
3) The balance of Yin, Yang
4) Worship of polytheistic deities
5) Exercises
6) Ancestor worship.
II) Chinese folk religion focusing primarily on:
1) Worship of gods, immortals and demigods including historic figures immortalized in legend.
2) Body Alchemy using:
i) The Five Elements
ii) Divine Directions
iii) Herbalism
iv) Martial Arts
v) meditation
vi) Feng Shui
vii) other
3) Ancestor worship
4) Divination
5) Worship of sacred texts (Zhen dong, Shen dong, Yuan dong, Daozang, Zhuangzi and the Tao te Ching.
I hope this helps.

suggested reading:

Zen Shredding: Insights, Questions and Confessions of a Meditator and Novice Snowboarder on the pursuit of dreams, inspiration, passion and change.Fulfillment in life occurs as a result of the pursuit of our dreams and the cultivation of our awareness of the divinity that lies within... Read More >