JOEL - Here is what modern day LDS doctrine teaches about the nature of the Godhead.

God the Father; his Son, Jesus Christ; and the Holy Ghost form the Godhead, which holds the keys of power over the universe. Each member of the Godhead is an independent personage, separate and distinct from the other two, the three being in perfect unity and harmony with each other.

Joseph Smith said, "I have always declared God to be a distinct personage, Jesus Christ a separate and distinct personage from God the Father, and that the Holy Ghost was a distinct personage and a Spirit: and these three constitute three distinct personages and three Gods" (TPJS, p. 370).

Each member of the Godhead fulfills particular functions in relation to each of the others and to mankind. God the Father presides over the Godhead. He is the Father of all human spirits and of the physical body of Jesus Christ.

Jesus Christ, the Firstborn son of God the Father in the spirit and the Only Begotten son in the flesh, is the creative agent of the Godhead and the redeeming mediator between the Father and mankind. By him God created all things, and through him God revealed the laws of salvation.

The Holy Ghost is a personage of spirit who bears witness to truth. The Father and the Holy Ghost bear witness of the Son, and the Son and the Holy Ghost bear witness of the Father (3 Ne. 11:32; cf. John 8:18). The Holy Ghost is NOT the spirit of Jesus Christ, He is a separate entity. There is something called "The Light of Christ". This refers to the spiritual power that emanates from God and fills the immensity of space and enlightens everyone and prompts them to do what is right. However, it is not the same as the Holy Ghost or the Gift of the Holy Ghost.

These three separate beings comprise the Godhead. They are each called a God and together as a group can also be called God. Jesus was a God even before He received a body. The Holy Ghost has always been considered a God even though He does not have a body. This was necessary for these two beings in order for them to do what was needed for them to do. The rest of us must first gain a body before we can ever consider becoming a God ourselves.

Latter-day Saints worship God the Father AND Jesus Christ and pray to the Father in the name of Christ. We never pray to Jesus or the Holy Ghost, although as joint members of the Godhead they are aware of what we are praying about so they can be instrumental in the answers to our prayers.

Heavenly Father is the Father of our spirits. Jesus is considered our "Father" also in three separate ways.

He is sometimes called "Father" because of his role as Creator. He is the Father of this earth.

He is also known as "Father" through the spiritual rebirth of mankind. When we are "born again" unto Christ we become known as the children of Christ, "his sons and daughters." He is the Father of our salvation (Mosiah 5:5-8; 15:10-13; 27:25-26; Alma 5:14).

He is also called Father because of his Eternal Parent investing him with power from on high and thereby alowing Him to represent our Heavenly Father.
Therefore, Heavenly Father is our Father and Jesus is also our Father.

Joseph Smith said: "It is the first principle of the Gospel to know for a certainty the character of God." "There are but very few beings in the world who understand rightly the character of God." (T.P.J.S., 345, 343)

There are prophets in the past, such as Brigham Young, who said things about the nature of God that seem to contradict with what has been said of other prophets, especially our more current prophets of today. I have always held to the belief that what our most current prophet says today is more important and more correct for us than what another one said over 100 years ago.
When prophets speak their own opinions on some subjects they may or may not be right. This really doesn't bother me that much, probably because of my strong testimony of the Gospel and my faith in the leadership of the Church.
I think that any differences that we have seen over the years in certain concepts (e.g. the nature of the Godhead for example) falls into that category of how God imparts His knowledge and eternal truths to us "line upon line, precept upon precept" .

"For behold, thus saith the Lord God: I will give unto the children of men line upon line, precept upon precept, here a little and there a little; and blessed are those who hearken unto my precepts, and lend an ear unto my counsel, for they shall learn wisdom; for unto him that receiveth I will give more; and from them that shall say, We have enough, from them shall be taken away even that which they have." (2 Nephi 28:30)

This goes not just for the members of the Church but also for the prophet and other leaders of the Church as well. And throughout the history of the Church we have "hearkened unto His precepts", and because of that He has given us more and more understanding as the scripture says. Because of this, what we know today sometimes seems to contradict with what others thought was true 100 years ago.