Buddhism began by encouraging its practitioners to engage in smrti. This is the kind of meditation that Buddha himself did in under the bodhi tree, and is referred to in the seventh step of the eightfold path. The bases for all meditation are shamatha and vipashyana.
Shamatha is often translated as calm abiding or peacefulness. It is the development of tranquility that is a prerequisite to further development. Vipashyana is special insight, and involves intuitive cognition of suffering, impermanence, and egolessness.
Only after these forms were perfected does one go on to the more hard-core kinds of meditation. Samadhi is concentration or one-pointed meditation. It involves intense focusing of consciousness.
Samadhi brings about the four dhyanas, (absorptions) Buddha refers to samadhi and the dhyanas in the eighth step of the eightfold path, and again when he died. Dhyana is rendered as Jhana in Pali, Ch’an in Chinese, Son in Korean, and Zen in Japanese, and has, in those cultures, become synonymous with meditation as a whole.
Having said all that it can be summed up thusly: Ananda, Buddha's cousin, once asked him if there was one particular quality one should cultivate that would best bring one to full awakening. Buddha answered: Being mindful of breathing.
"Breathing in long, he discerns that he is breathing in long; or breathing out long, he discerns that he is breathing out long. Or breathing in short, he discerns that he is breathing in short; or breathing out short, he discerns that he is breathing out short. He trains himself to breathe in sensitive to the entire body, and to breathe out sensitive to the entire body. He trains himself to breathe in calming the bodily processes, and to breathe out calming the bodily processes."
( copied and pasted from The Samyutta Nikaya 54.13)