THE BUDDHA'S EIGHTFOLD PATH:

The Buddha's method for spiritual development, which can ultimately lead to nirvana, or Enlightenment, is called The Eightfold Noble Path.  It is a process of perfecting eight fundamental qualities, or virtues: 1) Right Understanding, 2) Right Intention, 3) Right Speech, 4) Right Conduct, 5) Right Livelihood, 6) Right Effort, 7) Right Mindfulness, 8) Right Concentration.  This method, plus all of the other Buddhist teachings, derive from the Buddha's four fundamental principles, called The Four Noble Truths. [explanation].

A helpful starting point for effective practice is regular Meditation, which moves one toward serene stillness of the mind and body.  Meditation is ideally an effortless process, letting go of physical tensions and mental restlessness to achieve a centred, tranquil state of sensitive awareness.  But it's good to get proper instruction from an experienced practitioner, because a lot of additional factors affect the quality of your meditation -- for example, your breathing, your blood chemistry, your fitness, your energy level and your general state of health and restedness.

The Buddha's purpose behind such spiritual development is very down to earth: to get to a state beyond suffering.  Note that this is very different from the purpose of God-based religions.