Christianity was supposed to be about becoming like Jesus.  
We went in the wrong direction.
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What must I do to be saved?
 
The first thing that comes to mind when considering being "saved" is... saved from what? Saved from hell, saved from sin, saved from death? To consider this, we might first want to take a look at those people in the Old Testament who were faithful.
Were the Old Testaments saints saved?
The Old Testament saints (even ones as injudicious as Samson) described in Hebrews chapter 11 had faith, but did not come to completion.

And all of these, though they won divine approval by [means of] their faith, did not receive the fulfillment of what was promised, Because God had us in mind and had something better and greater in view for us, so that they [these heroes and heroines of faith] should not come to perfection apart from us [before we could join them].  Hebrews 11:9-40 (Amplified)

What happened to those who died in faith?  
And it came to pass, that the beggar died, and was carried by the angels into Abraham's bosom: the rich man also died, and was buried; And in hell he lift up his eyes, being in torments, and seeth Abraham afar off, and Lazarus in his bosom. And he cried and said, Father Abraham, have mercy on me, and send Lazarus, that he may dip the tip of his finger in water, and cool my tongue; for I am tormented in this flame.  But Abraham said, Son, remember that thou in thy lifetime receivedst thy good things, and likewise Lazarus evil things: but now he is comforted, and thou art tormented. And beside all this, between us and you there is a great gulf fixed: so that they which would pass from hence to you cannot; neither can they pass to us, that would come from thence. - Luke 16:22-26 (KJV)
When Jesus came He brought new life
Those in the Old Testament had the expectation of being resurrected and given a new body. Jesus told of a new life that would not require waiting in paradise for the resurrection.

Jesus saith unto her, Thy brother shall rise again. Martha saith unto him, I know that he shall rise again in the resurrection at the last day. Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live: And whosoever liveth and believeth in me shall never die. Believest thou this? - John 1:23-26

 

Essential salvation
We can see the bare essentials of salvation in the example of the thief on the cross. He is not baptized, brought into church membership, or made to repent of his sins. He simply believes (trusts) in Jesus.

And one of the malefactors which were hanged railed on him, saying, If thou be Christ, save thyself and us. But the other answering rebuked him, saying, Dost not thou fear God, seeing thou art in the same condemnation? And we indeed justly; for we receive the due reward of our deeds: but this man hath done nothing amiss. And he said unto Jesus, Lord, remember me when thou comest into thy kingdom. And Jesus said unto him, Verily I say unto thee, Today shalt thou be with me in paradise.  - Luke 23:39-43

  Salvation is a new life  
Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God. - John 3:3

for the law of the Spirit, that of the life in Christ Jesus, freed you once for all from the law of the sinful nature and of death. - Romans 8:2 (Wuest)

And so it is written, The first man Adam was made a living soul; the last Adam was made a quickening spirit. - 1 Corinthians 15:45

For as in Adam all die, even so in Christ shall all be made alive. - 1 Corinthians 15:22
We receive salvation when we trust in Jesus
And the keeper of the prison awaking out of his sleep, and seeing the prison doors open, he drew out his sword, and would have killed himself, supposing that the prisoners had been fled. But Paul cried with a loud voice, saying, Do thyself no harm: for we are all here. Then he called for a light, and sprang in, and came trembling, and fell down before Paul and Silas, And brought them out, and said, Sirs, what must I do to be saved? And they said, Believe on the Lord Jesus Christ, and thou shalt be saved, and thy house. - Acts 16:27-31

"believe" = pisteuō= trust in and rely on.

 

Salvation brings us out of death
Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life. - John 5:24

[Yes] we have confident and hopeful courage and are pleased rather to be away from home out of the body and be at home with the Lord. Therefore, whether we are at home [on earth away from Him] or away from home [and with Him], we are constantly ambitious and strive earnestly to be pleasing to Him. - 2 Corinthians 5:8-9

  Salvation breaks the power of sin over us  
We know that our old (unrenewed) self was nailed to the cross with Him in order that [our] body [which is the instrument] of sin might be made ineffective and inactive for evil, that we might no longer be the slaves of sin. - Romans 6:6

 
Salvation gives us eternal life in Jesus
1Th 4:17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.

1Jn 3:2 Beloved, now are we the sons of God, and it doth not yet appear what we shall be: but we know that, when he shall appear, we shall be like him; for we shall see him as he is. 

 

How are salvation and faith related?
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast. - Ephesians 2:8-9

I have been crucified with Christ [in Him I have shared His crucifixion]; it is no longer I who live, but Christ (the Messiah) lives in me; and the life I now live in the body I live by faith in (by adherence to and reliance on and complete trust in) the Son of God, Who loved me and gave Himself up for me. - Galatians 2:20 (Amplified)

  What is faith?  
Our salvation does not require advanced learning, special training, or strength of will. It is so simple and basic that any child can do it as easy as jumping into his father's open arms.

Pro 3:5 Trust in the LORD with all thine heart; and lean not unto thine own understanding. 

We trust in the person and character of Jesus, the promises of God, and the reality of the truth of His word.
Isn't just believing enough?
For whosoever shall call upon the name of the Lord shall be saved. - Romans 10:13

In the Roman empire, most people were slaves. If an official like a soldier questioned you, you might say, "I belong to Casius, he sent me here". This would be an example of calling on the name. To whom do you belong? Can he save you?