the LDS perspective on prayer [and revelation]

prayer
Prayer is an important aspect of living life as a Latter Day Saint. If you read my post "How to be a Muslim, Mormon or Christian for 30 Days" you have seen that prayer is important in any religion that I've studied, and no less emphasized in Mormonism.

Personal prayer: morning and night
Couple prayer (if married): morning and night
Family prayer (if applicable): morning and night
Meal prayers: at each meal

The Mormons believe that God wants to communicate with us: he loves us, he knows our needs, and he wants us to communicate with him through prayer. Although there are not prescribed prayers in Mormonism, instructions are given to them about how to pray:

1. Make the prayers meaningful and sincere.

“[If someone] shall pray and not with real intent of heart . . . it profiteth him nothing, for God receiveth none such” (Moroni 7:9).
“[pray with] with all the energy of heart” (Moroni 7:48)

2. Use appropriate reverence and respect when speaking to God.

Use language that shows love, respect, reverence, and closeness. Use the pronouns of the ((King James)) scriptures when we address God—Thee, Thou, Thy, and Thine, rather than the more common pronouns you, your, and yours...When we pray, we should use words that appropriately convey a loving, worshipful relationship with God. (LDS Study Topics Reference) 

3. Be thankful in prayer.

“live in thanksgiving daily, for the many mercies and blessings which he doth bestow upon [us]” (Alma 34:38)

4. Pray for others and their needs and/or salvation.

 “[we should pray] for [our] welfare, and also for the welfare of those who are around [us]” (Alma 34:27).

5. Seek guidance and strength in daily prayer.

6. Alongside prayer, action is required.

Our prayers for our own welfare and for the welfare of others will be in vain if we “turn away the needy, and the naked, and visit not the sick and afflicted, and impart of your substance, if ye have, to those who stand in need” (Alma 34:28).

Personal, private prayer is emphasized in Mormonism. They take the instruction from Jesus to: "Enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly” (Matthew 6:6) very literally, and while they may not pray in an actual closet (although I know some who do), they are definitely alone when they pray.
Incidentally, the only time Mormon missionaries in the field are left alone is during their morning and evening personal prayer time. At all other times, they have an assigned companion who sticks with them like glue.

Personal prayer time is encouraged by the church to be both on the knees as well as vocal - out loud.

Additionally, family prayer time, kneeling and praying out loud as a family, is an important tenet and should be done every morning and every evening. Not only do they believe that this strengthens the family bond, but it instills in the younger family members the habit of prayer  as well as the knowledge of how to pray.

revelation
The Mormons believe strongly that prayer is answered. Prayers are heard by God, and God replies either by intervening miraculously in the situation prayed about, or by speaking direction to the prayer. "Revelation" is the term used to describe the communication from God to man. Prophets are the only people who can receive a revelation for the church ((assumedly to cut back on confusion)) and the church has this to say about the Prophet (who is currently Thomas Monson, as of 2008):

As members of The Church of Jesus Christ of Latter-day Saints, we are blessed to be led by living prophets—inspired men called to speak for the Lord, as did Moses, Isaiah, Peter, Paul, Nephi, Mormon, and other prophets of the scriptures. We sustain the President of the Church as prophet, seer, and revelator—the only person on the earth who receives revelation to guide the entire Church. We also sustain the counselors in the First Presidency and the members of the Quorum of the Twelve Apostles as prophets, seers, and revelators.

...But, regular people can receive revelation for their own person and family. Since the men are the leaders of their family, they receive revelation for their family like the Prophet receives revelation for the church. And anyone who has been baptised and thereby filled with the Holy Spirit can receive revelation for themselves.

Of course, the word "revelation" is used in a context today where we consider that communication something large and life-changing. Like "I'm going to have a baby... and it belongs to your brother." or "Mom, Dad, I'm a lesbian." Revelation in the context of Mormonism can be something as simple as direction on which job to take, or guidance in daily life.

I kind of like the idea of revelation on a daily basis - God, revealing himself to us, in our daily walk, our day-to-day life: pieces of God and his love for us gathered throughout our lives.