One of the things that James is famous for--maybe even infamous for--is the teaching that faith by itself is not enough to make you right with God. "You see that a person is considered righteous by what they do and not by faith alone." (2:24). Wait a minute! Doesn't this statement go directly against that great teaching of Martin Luther and the Reformation: "justification by faith alone" (sola fide)?
Luther himself wondered as much in the early 1500s, when he accidentally started the Protestant movement. In 1522, when he first translated the New Testament into his own language of German, he put the book of James at the end with other books he didn't think were as solid as Paul and the earlier parts of the New Testament.  He considered it to be an "epistle of straw" because it seemed to pull against what he thought Paul taught. Meanwhile, when Luther was translating Romans 3:28, he added the word "only," which isn't there in the original Greek: "a man becomes right without works of law, through faith alone." 
It is a striking contrast, isn't it:
Paul: "A person is justified by faith apart from the works of the law" (NIV).
James: "a man is justified by works and not by faith alone" (NASB).
Now I don't personally think that Paul and James really contradict each other. But I do wonder if James thought he did! For me, it is hard to read what James has to say in James 2--especially the way he uses the same exact verse from Genesis about Abraham that Paul does (Gen. 15:6)--and not think that he is sparring at least with what he thinks Paul is teaching. You might say that James is arguing against a perverted version of Paul.
Why don't they contradict each other? They don't contradict because true faith for Paul absolutely entails righteous living. Similarly, the kind of "faith" that James is attacking is a mere belief without anything to show for it.
It helps to know that the same word can have more than one meaning. In fact, the different meanings of a word don't even need to have any relation to each other. Over time, words go wherever we take them, and their new meanings don't have to have anything with what they meant originally.
The different meanings of the word "faith" are actually somewhat similar to each other. So faith can be the pure "head knowledge" of James 2:19--"You believe that there is one God. Good! Even the demons believe that—and shudder." The word "believe" in Greek here is pisteuo, which is related to the word for faith (pistis). To believe, in Greek, basically means "to have faith," here in the sense of having a belief.
This is the kind of faith that James says cannot justify you or make you okay with God. The demons believe that God exists. They would no doubt get 100% on any test you gave them about God, creation, or pretty much anything to do with theology. But Jesus was not their Lord. They had not put their faith in Jesus or God.
For Paul, faith involved a reliance on and a commitment to Christ. "If you declare with your mouth, 'Jesus is Lord,' and believe in your heart that God raised him from the dead, you will be saved" (Rom. 10:9). Declaring someone your "Lord" is not some "scout's honor" or "pinky swear" that doesn't really matter. A Lord is a master, the kind of person you go and die in battle fighting for.
When Paul talks about "believing" that God raised Jesus from the dead, he means you are buying the whole deal. God raised Jesus from the dead and installed him as King of Kings over the whole universe. That is what you are declaring when you declare Jesus as Lord. You are, as it were, swearing your allegiance to the King. 
By contrast, James is concerned with the person who says all the right things, believes all the right things, but their life has nothing to show for it. The demons, he says, have that much faith, and they're still pretty scared. "Faith without deeds," James says, "is useless" (2:20). "As the body without the spirit is dead, so faith without deeds is dead." (2:26).
What does it mean for faith to have works? It means that if you see someone who is hungry or someone who barely has clothes, you do something about it. He puts it this way later: if you know the good you ought to do and you don't do it, that's what sin is (4:17). A man named John Wesley in the 1700s recognized this central sense of what the New Testament really means when it talks about doing wrong. The "sin" that God was really concerned about was any "voluntary transgression of a known law" of God."  In other words, when you know what God wants you to do (or not do) and you do the opposite.
James goes further to say that it is not good enough just to keep one part of God's will really well. For example, it is not enough to be really good at not stealing if you are constantly having affairs on your spouse. And it is not good enough to be really good at not killing if you hoard all the wealth God has given you and do not help those in need. This is what James means when he says, "whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it" (2:10).
One thing is to be sure. James and Paul both agree that you will be doing the right thing if you love your neighbor (2:8). This is the "royal" law. As Paul says, "Love does no harm to a neighbor. Therefore love is the fulfillment of the law" (Rom. 13:10).
How do we apply these truths to today?...
 Namely, Hebrews, Jude, and Revelation.
 My translation
 Another difference between Paul and James to keep in mind is that when Paul talks about "works of Law," he was especially concerned with those parts of the Jewish Law that distinguished Jew and Gentile. So in Galatians, the main point of discussion is circumcision. Paul wants the Galatians to know that "works of Law" (i.e., like circumcision) cannot make them right with God.
 Wesley says this several places. For example, in a sermon called, "On Perfection."