What is the Plan of Salvation in LDS theology? I know it's different than most Christian faiths' beliefs, and I know the missionaries teach it... I know it's a big part of Mormon curriculum and doctrine, and this site is replete with questions about seemingly every part of it, but would someone connect the dots and piece it together here in an overall summary? Why is it needed in LDS doctrine, what questions does it answer?
The LDS Plan of Salvation can be found on the official LDS website here.

In summary, the following are the main points:


We all once lived as spirit children of God in our premortal life.  While we were in our Premortal life, our Heavenly Father presented us with his plan of happiness, as described in Abraham 3:22-26
We chose, in our premortal life, to come to this earth, this existence, to follow the plan of Eternal Progression.  We are now in our Mortal Life.  During our mortal life, we are able to grow in ways we couldn't in our premortal life. The purpose of our current life is to grow, to prepare to be worthy of eternal life, to prove ourselves worthy, and to help others to know of God's plan.
When we die, we will be judged and received into a Kingdom of Glory.  The level of glory we inherit will depend on the depth of our conversion and our obedience to the Lord's commandments


This, of course, only scratches the surface, and the LDS Plan of Salvation encompasses not only salvation, but exaltation.

The most basic LDS explanation of what Salvation is:


  In the doctrine of The Church of Jesus Christ of Latter-day Saints,
  the terms “saved” and “salvation” have various meanings. As used in
  Romans 10:9-10, the words “saved” and “salvation” signify a covenant
  relationship with Jesus Christ. Through this covenant relationship,
  followers of Christ are assured salvation from the eternal
  consequences of sin if they are obedient. “Salvation” and “saved” are
  also used in the scriptures in other contexts with several different
  meanings.


There are actually six definitions of Salvation in LDS theology, all defined here. (Click the "view more" link.)


Salvation from Physical Death
Salvation from Sin
Being Born Again
Salvation from Ignorance
Salvation from the Second Death
Eternal Life, or Exaltation


A somewhat shorter version than the one linked to at the beginning of the article can be found here.

As for how one achieves Salvation, the teaching differs from mainstream Christianity.  Whereas the vast majority of Christianity believes that salvation is by Faith alone, with no works attached, LDS teaching is different. In LDS theology, only General Salvation is attained through Faith in Christ alone. 

From Elder Theodore M. Burton

Assistant to the Council of the Twelve
July 1972:


  As I listened to the radio a few days ago, I heard a minister tell his
  listeners: “Confess Christ and you shall be saved. Admit Christ into
  your heart and he will save you.”
  
  Then he quoted Ephesians 2:8 for his clinching argument: “For by grace
  are ye saved through faith; and that not of yourselves: it is the gift
  of God.” [Eph. 2:8]
  
  Then he gave his final advice: “Is this too much to ask of you?
  Thousands and hundreds of thousands have found lasting peace and
  happiness by accepting Christ as their Savior. Join with us in
  Christian faith and you shall be saved.”
  
  I wonder how many people have been lulled into a false sense of
  security by such teaching. As a missionary knocking at the doors of
  people, I had literally hundreds of people tell me that they were not
  interested in learning more about Jesus Christ, for they were already
  saved. The shocking thing about this is that they were right. What
  that minister said was true, but the difficulty is that it was not the
  whole truth.
  
  ...snip...
  
  The true value of the sacrifice of Christ means much more than this
  general salvation which comes to all mankind. There is an additional
  salvation that God has planned for his children. This additional
  salvation is an individual salvation and is conditioned not only upon
  grace, but also upon obedience to gospel law. One of the prophets in
  the Book of Mormon explained why he and his associates were so
  concerned about teaching more about Jesus Christ, as he wrote:


So the general salvation is through faith in Christ alone, but that's just the beginning.  There are, in Salvation, more than one level of Glory, which is, as stated above "conditioned not only upon grace, but also upon obedience to gospel law.".

However, this is not seen within LDS teaching as a works-based salvation, even at this level.  There is somehow, in LDS theology a difference between obedience, and earning your way in.  More from the article quoted above expands upon this.


  Exaltation comes as a gift from God, dependent upon my obedience to
  God’s law. No works I do solely of my own power can bring this to
  pass. Only by the grace of God has this course been opened to me, but
  only through obedience to the laws of God can I claim my inheritance
  in the celestial kingdom of my Heavenly Father as a son within his
  family. I cannot be exalted in my sins, but must work until I overcome
  them.
  
  Amulek the prophet explained this most clearly as he said of God:
  
  “And I say unto you again that he cannot save them in their sins; for
  I cannot deny his word, and he hath said that no unclean thing can
  inherit the kingdom of heaven; therefore, how can ye be saved, except
  ye inherit the kingdom of heaven? Therefore, ye cannot be saved in
  your sins.” (Alma 11:37.)


But later on in the article, Burton again teaches that works are a result of faith.  But the fact remains that in LDS theology, works are required. Perhaps not as a way of "buying" our way in, but as a sign, in that, if we don't have works, it's a sure sign that we don't have faith. Often, the following is quoted as support for this belief.


  James 2:14-26 (KJV)
  
  14 What does it profit, my brethren, if someone says he has faith but
  does not have works? Can faith save him? 15 If a brother or sister is
  naked and destitute of daily food, 16 and one of you says to them,
  “Depart in peace, be warmed and filled,” but you do not give them the
  things which are needed for the body, what does it profit? 17 Thus
  also faith by itself, if it does not have works, is dead.
  
  18 But someone will say, “You have faith, and I have works.” Show me
  your faith without your[a] works, and I will show you my faith by
  my[b] works. 19 You believe that there is one God. You do well. Even
  the demons believe—and tremble! 20 But do you want to know, O foolish
  man, that faith without works is dead?[c] 21 Was not Abraham our
  father justified by works when he offered Isaac his son on the altar?
  22 Do you see that faith was working together with his works, and by
  works faith was made perfect? 23 And the Scripture was fulfilled which
  says, “Abraham believed God, and it was accounted to him for
  righteousness.”[d] And he was called the friend of God. 24 You see
  then that a man is justified by works, and not by faith only.
  
  25 Likewise, was not Rahab the harlot also justified by works when she
  received the messengers and sent them out another way?
  
  26 For as the body without the spirit is dead, so faith without works
  is dead also.


And also, the lack of good works/righteousness as a sign of not really being Faithful is stressed in Matthew 15:8, which is heard in almost every Sunday School class I attended when I was attending the LDS Church.


  These people honor me with their lips, but their hearts are far from
  me.


Burton goes on to define those works: 


  Those works, which follow the true exercise of faith, include
  repentance, baptism, receipt of the Holy Ghost, and continued
  righteousness to the end of our lives.


Burton expands a bit on those who do not obey the Law in full:


  God said of those who were not willing to pay the full price of
  exaltation through full obedience to his whole law: “Therefore, when
  they are out of the world they neither marry nor are given in
  marriage; but are appointed angels in heaven, which angels are
  ministering servants, to minister for those who are worthy of a far
  more, and an exceeding, and an eternal weight of glory.


This is the opposite of Mainstream Christianity, which believes that as imperfect beings, we cannot be fully obedient, and thus is the distinction - the splitting of hairs between the "mainstream" understanding of "by faith alone".  Mainstream Christianity says "I can never be good enough to add a single iota to my salvation.  I am miserable and wretched, and I rely solely on God's mercy because even my righteousness is as filthy rags to Him."   The LDS teaching, on the other hand, is that we must be fully obedience, and we are able to be fully obedient, and those that achieve this attain the highest form of exaltation.