Joseph Smith said, "We here observe that God is the only supreme governor and independent being in whom all fullness and perfection dwell; who is omnipotent, omnipresent, and omniscient; without beginning of days or end of life; and that in him every good gift and every good principle dwell; and that he is the Father of lights; in him the principle of faith dwells independently, and he is the object in whom the faith of all other rational and accountable beings center for life and salvation." (Lectures on Faith, Lecture Second).
As someone who saw God the Father and God's Son Jesus Christ, Joseph was qualified in a way relatively few others were to talk about the nature of God. It is important to understand God's nature so that our faith in Him is what it can and should be. Traditionally in The Church of Jesus Christ of Latter-day Saints we refer to God as Heavenly Father, focusing on His Fatherhood, for we are His actual spirit children. Again, understanding the nature of God is important to our faith in Him.
Joseph Smith taught, "Let us here observe, that three things are necessary in order that any rational and intelligent being may exercise faith in God unto life and salvation. First, the idea that he actually exists. Secondly, a correct idea of his character, perfections, and attributes. Thirdly, an actual knowledge that the course of life which he is pursuing is according to his will. For without an acquaintance with these three important facts, the faith of every rational being must be imperfect and unproductive; but with this understanding it can become perfect and fruitful, abounding in righteousness, unto the praise and glory of God the Father, and the Lord Jesus Christ." (Lectures on Faith, Lecture Third).
Joseph Smith went on to write of the character of God: He was before the world was created, He is merciful and gracious, He changes not, He is truthful and cannot lie, He is no respecter of persons (meaning that "in every nation he that fears God and works righteousness is accepted of Him"; this means that He is "not a respecter of persons" insofar as those persons are righteous), and God is love.
Of the attributes of God the Prophet Joseph said that God has knowledge, faith (or power), justice, judgment, mercy, and truth. All study of the nature of God should increase our faith in Him.
On one bright spring morning in 1820 Joseph Smith, a 14 year old boy, went into a grove of trees near his home. As he knelt down in prayer he was attacked by the devil, who tried to stop Joseph's prayer and end Joseph's life. Suddenly a light appeared from heaven, dispelling the darkness and Satan. In the midst of this light appeared two beings, first one then shortly afterward, another. The first called Joseph by name and pointed to the other saying, "This is my Beloved Son, hear Him!" We do not know how long the visit lasted - it could have been a minute or many. In that short time Joseph learned more about the nature of God than had been known on earth for more than a thousand years. Joseph knew God the Father and Jesus Christ were two separate beings. He witnessed their glory and heard their voices. He viewed their countenances and knew that they knew him as an individual. They knew Joseph's name. They cared for him and loved him as they do each of us. Of all the things that the Prophet Joseph did (and "Joseph Smith, the Prophet and Seer of the Lord, has done more, save Jesus only, for the salvation of men in this world, than any other man that ever lived in it."; D&C 135:3), one of the greatest things he did was reveal unto the world the true nature of God.
Much of God's nature is found in the Bible but over the years creeds and discussions and contentions led to distortions of people's conceptions of God. We know that we are created in the image of God (see Genesis 1:26-27) but the added knowledge gained from the Book of Mormon (read, for example, about the experience the brother of Jared had when he saw the Lord on a mountain top: Ether 3:6-16), the Doctrine and Covenants (see D&C 76), and the Pearl of Great Price (see Abraham 4:26-27, for example). Countless prophetic declarations since Joseph Smith's day have further witnessed of what Joseph taught.
God created the universe. We know He did this through the power of His priesthood but beyond that we do not know how He did it. Was it created in the manner that science teaches? Maybe. Was it created in six 24 hour days? No (read in the book of Abraham for clarification: "And the Gods watched those things which they had ordered until they obeyed. And it came to pass that it was from evening until morning that it was night; and it came to pass that it was from morning until evening that it was day; and it was the fourth time."; Abraham 4:18-19). God has all power yet He is not distant or disinterested in us. He knows us individually.
As we better understand God we will know of His love for us (see John 3:16), which love is manifest most strongly through His Beloved Son Jesus Christ (who is just like His Father; see John 14:6-9). As we feel God's love we can continue to grow in faith and knowledge of Him. We can grow and progress to be like Him. He is our Father in Heaven and wants us to become like Him and to return to live with Him again.