There are many discourses on meditation, but the Satipaṭṭhāna Sutta is perhaps the most important one. Sati means “mindfulness” or “awareness,” and upaṭṭhāna means setting up or “establishing.” So the discourse is about the setting up of mindfulness.
There are four foundations of mindfulness: 1) Body, 2) Feelings, 3) Thoughts, and 4) Mental phenomena.
Mindfulness of the Body
Mindfulness of respiration (ānāpānassati) is just one of several meditation objects in the section on mindfulness of the body. One can also contemplate the four postures of standing, walking, sitting, or lying down, or all daily activities such as moving the limbs, looking here and there, eating, drinking, etc.
The Mahāsi meditation method analyses the body in terms of the four elements: earth (solidity), water (fluidity), fire (temperature), and air (motion). In sitting one contemplates the element of motion in the rising and falling movements of the abdomen; in walking meditation one observes the element of motion in the movements of the feet.
Less frequently taught methods analyse the body in terms of its 32 repulsive components: head hair, body hair, nails, teeth, skin, etc., or compare it to corpses in various stages of decay.
Mindfulness of Feelings
“How, monks, does a monk dwell contemplating feelings? Here, monk, a monk, when feeling a pleasant feeling he knows, ‘I feel a pleasant feeling.’ When feeling a painful feeling he knows, ‘I feel a painful feeling.’ When feeling a neutral feeling he knows, ‘I feel a neutral feeling.’ When feeling a pleasant sensual feeling he knows, ‘I feel a pleasant sensual feeling.’ When feeling a pleasant non-sensual feeling he knows, ‘I feel a pleasant non-sensual feeling.’ When feeling an unpleasant sensual feeling he knows, ‘I feel an unpleasant sensual feeling.’ When feeling an unpleasant non-sensual feeling he knows, ‘I feel an unpleasant non-sensual feeling.’ When feeling a neutral sensual feeling he knows, ‘I feel a neutral sensual feeling.’ When feeling a neutral non-sensual feeling he knows, ‘I feel a neutral non-sensual feeling.’”
Mindfulness of Thoughts
A meditator must also be mindful of thoughts (cittānupassana satipaṭṭhāna). Knowing a lustful thought as a lustful thought, an angry thought as an angry thought, etc. Before being able to do this effectively, one should first establish mindfulness on the body and on feelings.
Mindfulness of Mental Objects
The five hindrances — sensual desire, ill-will, laziness, restlessness, and doubt — are one aspect of mindfulness of mental objects. Positive states such as energy, joy, tranquillity, bliss, equanimity should also be contemplated and known whenever they occur.
What is Insight?
Insight is the wisdom that arises when concentration and mindfulness have been firmly established on one or more of the four foundations of mindfulness. When one is able to observe mental and physical phenomena with equanimity, one can see them as they truly are (yathābhūta ñāṇadassana), revealing the three universal characteristics of impermanence (anicca), unsatisfactoriness (dukkha), and not-self (anatta).
Until one reaches this relatively high stage, one is not really practising insight meditation, but just establishing mindfulness. However, if you wish to call it “insight meditation” because that is your final goal, then that’s fine too, even though no insight has yet been gained.