Please excuse me for a large answer, in my opinion this question is really hard to answer in several words.
Althought there are many references to "meditation" in Bible, however, word "meditation" should be used very carefully here, to be not confused with meditation practice in eastern religions, such as Buddhism or Hinduism.
We Christians should listen to the Church, the only authority of faith on the Earth. And both Catholic and Orthodox Church warns about mixing prayer with any New Age practicies.
Catholic Church about meditation
Letter to the Bishops of the Catholic Church on some aspects of Christian meditation
"This document of the Congregation for the Doctrine of the Faith
stresses the differences between Christian and eastern meditative
approaches. It warns of the dangers of attempting to mix Christian
meditation with eastern approaches since that could be both confusing
and misleading, and may result in the loss of the essential
Christocentric nature of Christian meditation.
The letter warns that "euphoric states" obtained through Eastern
meditation should not be confused with prayer or assumed to be signs
of the presence of God, a state that should always result in loving
service to others. Without these truths, the letter said, meditation,
which should be a flight from the self, can degenerate into a form of
self-absorption. The letter warns against concentration on the self,
rather than on Christ, and states that:
Christian prayer, ..., the communion of redeemed creatures with the
intimate life of the Persons of the Trinity, based on Baptism and the
Eucharist, source and summit of the life of the Church, implies an
attitude of conversion, a flight from "self" to the "You" of God. Thus
Christian prayer is at the same time always authentically personal and
communitarian. It flees from impersonal techniques or from
concentrating on oneself, which can create a kind of rut.
The letter also warns that concentration on the physical aspects of
meditation "can degenerate into a cult of the body" and that equating
bodily states with mysticism "could also lead to psychic disturbance
and, at times, to moral deviations."
A Christian reflection on the New Age, a six year study by the Roman Catholic Church on the New Age movement
The document states that for Christians, the spiritual life is a
relationship with God. It criticizes Eastern meditation and states
that all meditation techniques need to be purged of presumption and
pretentiousness. It states that Christian prayer is not an exercise in
self-contemplation, stillness and self-emptying, but a dialogue of
love, one which "implies an attitude of conversion, a flight from
'self' to the 'you' of God".
Orthodox Church about meditation
Easter meditation from the point of Orthodoxy and Science
The pursuit of imaginary grace of peace leads to irreparable spiritual
losses: "painlessness of a heart dazzles the mind" (St. John of the
Ladder, The ladder of divine ascent 7:13). We can find a confirmation
of this idea in the words of St. Peter of Damascus: "Lowliness of mind
is a product of intellect, and intellect is a product of temptations".
Optina elder Hieroschemamonk Makarios said that if we want to be
glorified with the Lord, then we must suffer with Him, we must suffer
with everything that He wills send to us.
Orthodoxy and the Faith of Future, monk-priest Seraphim Exposes that Transcendental meditation, introduced in USA by Maharishi, contains secret initiation as a pagan Guru worshipping cult
Christian meditation
A great article on that point in Wikipedia lists several practical approaches:
Within the Exercises, daily instructions include various meditations
and contemplations on the nature of the world, of human psychology as
Ignatius understood it, and of man's relationship to God through Jesus
Christ. The Exercises is divided into "four weeks" of varying lengths
with four major themes: sin, the life of Jesus, the Passion of Jesus
and the Resurrection of Jesus. During each day of the Exercises, a
typical retreatant prays with a particular exercise, as assigned by
the director, reviews each prayer, and, following four or five periods
of prayer, reports back to the spiritual director of the retreat who
helps them to understand what these experiences of prayer might mean
to the retreatant. The goal of the Exercises is to reflect upon their
experiences and to understand how these same experiences might apply
to the retreatant's life.
Her starting point was the practice of "recollection", i.e. keeping
the senses and the intellect in check and not allowing them to stray.
In her meditations, one generally restricts attention to a single
subject, principally the love of God. In The Way of Perfection she
wrote: "It is called recollection because the soul collects together
all the faculties and enters within itself to be with God". She would
use devices such as short readings, a scene of natural beauty or a
religious statue or picture to remind her to keep her focus. She wrote
that in due course, the mind naturally learns to maintain focus on God
almost effortlessly. St. Theresa viewed Christian meditation as the
first of four steps in achieving "union with God", and used the
analogy of watering the garden. She compared basic meditation to
watering a garden with a bucket, Recollection to the water wheel,
Quiet (contemplation) to a spring of water and Union to drenching
rain.
In the preparation part, one places oneself in the presence of God
and asks the Holy Spirit to direct the prayer, as in the Epistle to
the Romans[8:26]: "The Spirit helps us in our weakness, for we do not
know what to pray for, but the Spirit himself intercedes for us with
sighs too deep for words." In the consideration part, one focuses
on a specific topic, e.g. a passage from the Bible. In the
affections and resolutions part, one focuses on feelings and makes a
resolution or decision. For instance, when meditating on the Parable
of the Good Samaritan one may decide to visit someone sick and be kind
to them. In the conclusion part, one gives thanks and praise to God
for the considerations and asks for the grace to stand by the
resolution.
The 20th century has also witnessed a new focus on Biblical
meditation. These may be defined as: "the devotional practice of
pondering the words of a verse or verses of Scripture with a receptive
heart."
Modern Biblical meditations may be designed to relate and connect the
Biblical message to the modern world.
Such Biblical meditations may correspond to specific seasons such as
Lent with the meditation topic selected to interact with two or three
readings of the Bible during weekdays or Sundays of Lent.
The meditation sequence may begin by a summary of the Bible reading,
then suggest specific ideas for meditation, then conclude with an
appropriat prayer.
Such meditations may also be designed not just for "strong seasons"
such as Lent or Easter, but also for Ordinary Time.
In the 20th century methods of Christian meditations have been taught
using relatively new devotions such as the Divine Mercy devotion.