If one were to point to a single meditation technique most characteristic of East Asian contemplative practice, it would be focusing on the breath. There are many ways to do it. Here is one.
Sit in accordance with the instructions in the posture article. Close your eyes. Settle into the sitting posture for a moment.
Now focus your attention on body sensations associated with the breath. This might include the rise and fall of the chest, the movement of the abdomen, the feeling of air moving in the nose, the throat, or across the upper lip.
Now pick the body sensation associated with the breath that is easiest for you to detect and narrow your focus to cover just that body sensation, ignoring everything else. Ignore any thoughts that might arise (without trying to turn them off), ignore outside sounds, ignore body sensations other than your chosen breath sensation. Try to keep your attention continuous. If your mind wanders, (likely in the beginning) just gently bring it back to the breath.
Sometimes there is a tendency to control the breath, particularly if you have a history of yoga or other breath control practices. But in this case, try to let go of the need to control the breath. Just allow it to find its own pace and depth. Your only job is to keep your attention focused on it.
You may be able to increase your concentration power (reduce wandering) by counting the breath. Count silently to yourself: one on the inhalation, two on the exhalation, three on the next inhalation, and so on until you reach ten. Then count backwards from ten to one and begin again. Continue in this way.
This method is simple but is powerful enough to last you a lifetime.
One of the two most important meditation practices to come out of Burma is the noting practice of the Mahasi Sayadaw lineage. This section will describe a noting practice.
Most of sensory experience can be divided into three categories, visual, auditory, or somatic. These three categories can be further divided into objective and subjective. Objective visual experience is eyes-open sight while subjective visual experience is mental image or visual thinking. Objective auditory experience is the sound of the external world while subjective auditory experience is mental talk or verbal thinking. Subjective somatic experience is body sensation of emotional origin while objective somatic experience is all non-emotional body sensation. With that background we can assign simple labels to sensory experience, labeling any visual experience, objective or subjective, with the word "see". Any auditory experience can be labeled "hear". And any somatic experience can be labeled "feel".
Sit, as described in the article on sitting posture. This will be an eyes-open practice. Allow your attention to move freely throughout all sensory experience. Wherever your attention is drawn, let it go there.
If your attention is drawn to visual experience (either sight or mental image) say "see". If your attention is drawn to auditory experience (either sound or mental talk) say "hear". If your attention is drawn to somatic experience (any body sensation) say "feel".
When first learning this technique, speak your labels out loud if your circumstances permit. Otherwise say the labels silently to yourself. Try to label using a tone of voice and pace that is gentle and tranquil to help invite equanimity.
And that's it. There are, of course, more details and subtleties as you advance. But this is enough to start you on your way with a noting practice.