"If you really want to see for yourself what the Buddha was talking about, you don't need to bother with books. Watch your own mind." - Ajahn Chah, Thai Monk of the Theravada tradition and cofounder of the Chithurst Monastery in Sussex, England.
It is this advice that aspiring Buddhists find to be both greatly difficult and highly rewarding. One can fill themselves with immense scholarly knowledge of Buddhism while experiencing none of its insights. On the other hand, one may know nothing of the Dharma or the Buddha yet know firsthand the wisdom that they teach.
The best way I can suggest of immediately experiencing this is to simply close your eyes and follow your breath - from its initial entrance into your mouth or nose, down into the depths of your lungs, and slowly back out. You may want to internally count each exhalation and see if you can get to 10 without any non-related thoughts arising. If you can, congratulations! You already have developed a calm mind, fertile ground for awareness to bear its fruit. If you are like most people, however, you completed a few full breaths, followed a side-thought off somewhere, then realized your err and resumed counting (this may have happened a couple times en route).
To experience one of the more powerful insights associated with Buddhism, some degree of practice is most likely necessary. Wildmind.org provides a wonderful structure for such practice.
However, as mentioned above, meditation itself is not entirely necessary for one to develop insights into the Truths of existence. While meditation is the practice prescribed by the Buddha to his disciples as a way of developing awareness, such an awareness can be cultivated in simple daily life. It is awareness and concentration that unlock the doors of wisdom in the Buddhist tradition; if one is skilled in these they will grow to understand the purpose of such things as meditation, rituals, scholarship, and the likes.
Too often our minds are too clouded with frivolous, repeated thoughts to operate at our highest capacity. Yet each of us has experienced a time when our minds felt truly lucid and expansive. For many this comes most easily at times of artistic expression, such as painting or writing poetry. This is how I imagine the enlightened mind to be at all times. But while the artist's lucidity is capable of being interupted mid-stream, the enlightened mind is imperturbable. Just as a great painter's brush can manipulate a canvas and a poet may expand a reader's mind, the enlightened individual's impact is without substance, without direction, and without bounds.
From the "Buddhism is..." page (7 May, 2005):
Fifth is the claim that Buddhism is experientially based. I think this is another possible redundancy, after exploratory, but there might be a couple new points to be made. In Buddhism it can be said that ultimate truth is a matter of experiencing the world 'as it truly is'. This means digging through all of our cultural, societal, etc conceptual baggage and 'returning' to a direct awareness of the world. In Buddhism, this is not just philosophical talk, it is something TO BE DONE. It is done through meditation, hours and hours of meditation. Through sitting silently and observing our mind at work (without all of the world around to keep it somewhat pinned down), we see that our perceptions of the world are only made through a bit of a fog, or better, we see the world as though through a dirtied mirror. Meditation acts to clean that mirror, so that what we see is actually the world, 'as it truly is'.
Things are not to be taken on 'blind' faith ever in Buddhism. Faith is an important concept in Buddhism, but really the Buddhist term should be translated as 'confidence' which includes most importantly, self-confidence. If you don't believe that you can make progress in life, that you can overcome consumerism, destructive relationships, personal issues, etc, then you simply won't be able to. Confidence is the necessary first step (actually second, first you must realize there is a problem to overcome!). Through confidence and some meditation (if done properly) joy arises. You WILL experience something, and this gives more confidence, as you will have seen for yourself a bit of the result. Through further meditation you can move beyond joy (which is in a sense momentary) to a sustained joy (rapture), then to an overall feeling of calm happiness (like a child being hugged by his/her mother after a tough day, or a warm fire and a cup of hot chocolate after a winter day in Montana - point being that it fills your whole body with warmth and security). After this, if one maintains focus, one enters 'bliss', a sort of one-pointed version of the previous feeling (all of the goodness is condensed into a single point and your whole attention is suffused by this). Finally, one enters one-pointedness, where the 'good' quality of the prior sensation falls away and all that remains is the attention. Now one has accomplished the fourth jhana, or absorption, and is quite far on the Buddhist meditative path. From here one goes on, cognitively, to explore reality with this laser-like focus. One also develops the ability to 'call up' states of joy, rapture, bliss and concentration at will, which is extremely useful in city traffic or when working on a long essay. For an in-depth read on meditation, try "The Path of Purification/Visuddhimagga" by Buddhaghosa, a 6th century Sri Lankan monk.
See the full "Buddhism is..." essay.