The meditation practice of Zen, called "zazen" in Japanese, is the heart of Zen. Daily zazen is the foundation of Zen practice.
You can learn the basics of zazen from books, web sites and videos. However, if you're serious about pursuing a regular zazen practice, I recommend that you sit with others at least occasionally; most people find it deepens the practice. If there's no monastery or Zen center handy, you might find a "sitting group" of laypeople who sit zazen together at someone's home.
As with most forms of Buddhist meditation, beginners are taught to work with their breath to learn concentration. Once your ability to concentrate has ripened -- expect this to take a few months -- you may either sit "shikantaza" -- which means "just sitting" -- or do koan study with a Zen teacher.
Why Is Zazen So Important?
Like many aspects of Buddhism, most of us have to practice zazen for a while to appreciate zazen. At first you might think of it primarily as mind training, and of course it is. If you stay with the practice, however, your understanding of why you sit will change. I can't tell you how it will change, because this will be your own personal and intimate journey, not mine.
One of the most difficult parts of zazen for most people to comprehend is sitting with no goals or expectations, including an expectation of "getting enlightened." Most of us do sit with goals and expectations for months or years before the goals are exhausted and we "just sit." Along the way, you learn a lot about yourself.
You may find "experts" who will tell you zazen is optional in Zen, but such experts are dilettantes. I don't care how many degrees they have or how many books they've written; they are mistaken. This misunderstanding of the role of zazen comes from misreadings of Zen literature, which is common because Zen literature makes no sense to literal readers.
Why Zen Makes No Sense
It isn't true that Zen makes no sense. Rather, "making sense" of it requires understanding language differently from the way we normally understand it.
Zen literature is full of vexatious exchanges such as Moshan's "Its Peak Cannot Be Seen" that defy literal interpretation. However, these are not random, Dadaist utterings. Something specific is intended. How do you understand it?
Bodhidharma said that Zen is "direct pointing to the mind." Understanding is gained through intimate experience, not through intellect or expository prose. Words may be used, but they are used in a presentational way, not a literal way.
Zen teacher Robert Aitken wrote in The Gateless Barrier (North Point Press, 1991, pp. 48-49):
"The presentational mode of communication is very important in Zen Buddhist teaching. This mode can be clarified by Susanne Langer's landmark book on symbolic logic called Philosophy in a New Key. She distinguishes between two kinds of language: 'Presentational' and 'Discursive.' The presentational might be in words, but it might also be a laugh, a cry, a blow, or any other kind of communicative action. It is poetical and nonexplanatory - the expression of Zen. The discursive, by contrast, is prosaic and explanatory. … The discursive has a place in a Zen discourse like this one, but it tends to dilute direct teaching."
There is no secret decoder ring that will help you decipher Zenspeak. After you've practiced a while, particularly with a teacher, you catch on. Or not. Let me just say that the Web is peppered with academic explanations of koans that are painfully and horribly wrong, because the "scholar" analyzed the koan as if it were discursive prose.
So, how do you understand it? If you want to understand Zen, go face the dragon in the cave for yourself.
The Dragon in the Cave
Wherever Zen has established itself, it has rarely been one of the larger or more popular sects of Buddhism. The truth is, it's a very difficult path, particularly for laypeople. I don't think it's for everybody.
On the other hand, for a small sect Zen has had a disproportionate impact on the art and culture of Asia, especially in China and Japan. Beyond kung fu and other martial arts, Zen has influenced painting, poetry, music, flower arranging, and the tea ceremony.
Ultimately, Zen is about coming face-to-face with yourself, in a very direct and intimate way. This is not easy. But if you like a challenge -- check it out.