Our basic practice is Quiet Sitting. This is an inclusive spiritual practice that allows the mind to quieten and thoughts to settle. It is not particularly arcane or esoteric but is instead freely accessible to everyone. We begin by sitting with our buttocks on a small cushion and placing our knees on the floor, creating a stable posture. The spine is kept straight but so rigid as to create unnecessary strain.
The hands are place in the lap, with the back of the fingers of left hand resting atop the fingers of the right with the tips of the thumbs lightly touching, as if you were holding an invisible egg. Your head, which weighs roughly as much as a bowling ball, should be comfortably balanced atop your spine. According to tradition the the tip of the tongue may be placed lightly touching the roof of the mouth to decrease swallowing.
I am still not sure if this works.
The eyes may be close or left open. Find the one that creates the least distraction for you. For some people the eye lids are like tiny movie screens and when the eyes are closed all sorts of mental images begin to appear. For other people, and I tend to be of this kind, random patterns in wood grain, carpet or whatever quickly become panda bears, walruses, random politicians and whatever else the mind can make of them.
I am in general of the opinion that the practice should be adapted to the individual rather than adapting the individual entirely to the practice. If sitting on a cushion on the floor causes pain, adapt the instructions to a chair. If your back is naturally not straight, and mine is not, don't worry about it. The most important thing is simply finding a posture that strikes a balance between being alert and aware and being comfortable and relaxed. The former two is why lying down is normally not recommended.
You want your breaths to be natural and unforced and coming from your diaphragm. As you breathe in you should feel you belly expand and when you breathe out, it will naturally fall. Regardless of which method you choose next, you will want to take three or four mindful breaths before you proceed. As you do this, also do a quick mental inventory, double checking your posture making sure that you are comfortable and making a mental note of any possible sources of pain, discomfort or distraction. You want to avoid squirming but if something needs to be moved, move it.
What comes next tends to be a more personal nature. Many people count their breaths in sets of ten or so. They may count the in breaths and out breaths separately or they may just count the in breaths or out breaths. Whichever way they choose, when they reach ten, they return to one and start over. The goal is to keep the mind from wandering rather than counting to ten. When the mind wanders, simply bring your attention back to your breath.
Another method is to recite the name of Amida Buddha. In Japanese this is sometimes rendered 'Na Man Da Bu' and it is very easy to recite 'Na Man' on an in breath and 'Da Bu' on the out breath (or vice versa). Here the basic idea, which is part of Pure Land Buddhism, is that by being mindful of the Buddha in one moment, in the next moment we are closer to the Buddha. When the mind wanders, simply bring your attention back to 'Na Man Da Bu'.
(Should you wonder, 'Na Man Da Bu' is a contracted form of Namu Amida Butsu. Namo or Namu means to take refuge. Amida Butsu or Amida Buddha is the Buddha of infinite light called Amitabha in Sanskrit and is commonly found in the various Buddhist schools of Southeast Asia in some capacity or the other.)
Still other people will simply mentally say 'rising' as they breathe in and 'falling' as they breathe out, referring to the rising and falling of their abdomen. There are also metta and naikon meditation, which while beyond the scope of this introduction, may also be explored and practiced here. The absolute best practice, however... is the one that keeps you coming back to the cushion. What I like best about the concept of Quiet Sitting is that we can support each other on the path even though our approach to that path differs.
As for how long you should sit, that too is a matter of personal preference. Somewhere in American Buddhism, twenty minutes seems to have become standard. You may like to push it to 25 or 30 minutes. However it is probably better to stick to a shorter time that you can do often and regularly rather than sitting in erratic and unsustainable bursts. One of way to think of it is that 15 minutes represents roughly 1% of your day and giving something 1% of your time doesn't seem like such a big deal. During our group practice we sit for about twenty five minutes.