1. Saved by grace
   
   
   1. (Ephesians 2:8-9) - "For by grace you have been saved through faith; and that not of yourselves, it is the gift of God; 9not as a result of works, that no one should boast."
   
   
   2. (Rom. 3:20, 28) - "because by the works of the Law no flesh will be justified in His sight; for through the Law comes the knowledge of sin...28For we maintain that a man is justified by faith apart from works of the Law."
   
   
   3. (Galatians 2:16) - "nevertheless knowing that a man is not justified by the works of the Law but through faith in Christ Jesus, even we have believed in Christ Jesus, that we may be justified by faith in Christ, and not by the works of the Law; since by the works of the Law shall no flesh be justified."
   
   


2. Saved by works
   
   
   1. (James 2:24) - "You see that a man is justified by works, and not by faith alone."
   
   
   2. (Matthew 19:16-17) - "And behold, one came to Him and said, "Teacher, what good thing shall I do that I may obtain eternal life?" 17And He said to him, "Why are you asking Me about what is good? There is only One who is good; but if you wish to enter into life, keep the commandments."
   
   

God does not want a faith that is empty and hypocritical.  James 2 is talking about those who "say" that they have faith but have no works.  Therefore, people cannot tell if they are true believers or not, because there is no fruit.  That kind of a faith is useless and is not a saving faith.  True faith results in true works.

In Matthew 19:16-17, Jesus was speaking to a Lawyer who was self-righteous since he wanted to put Jesus to the test (Luke 10:25).  He asked what he must do in order to obtain eternal life and Jesus responded with the requirements of keeping the commandments.  If a person keeps all of the commandments, it would seem that they could obtain eternal life.  However, nobody can keep all of the commandments.  Therefore, Jesus' comments to this man show this man that justification can only be by faith since no one can keep all of the commandments.  This is why it says in Eph. 2:8 that we are saved by grace through faith.  Also, Romans 3:20,28 and Galatians 2:16 tells us that no one is justified in the sight of God by the law; that is, by the works that he can do.

There is no contradiction at all when we examine the contexts.  We are justified by faith but that faith must be alive (James 2).  The Law cannot save us because we are incapable of keeping it (Matthew 19:16-17).  Therefore, salvation is by grace through faith.

For more information, please see the paper Are we Justified by Faith (Romans) or by Works (James)?