How do we reconcile what Paul says about works with what James says?
Paul: We are justified by faith apart from works of law (Rom3:28)
James: We are justified by works not by faith alone (Jas2:24)
The short answer is that Paul is talking about people who want to justify themselves before God by their own efforts independent of Christ while James is talking about the opposite: people who hope they will be justified before God by Christ's efforts regardless of what they themselves do. James is condemning "faith alone", Paul is in effect condemning "works alone". Both attitudes are wrong. Neither results in justification before God.
Typical of the people Paul had in mind were those Jews who refused Jesus as their Messiah and still hoped to justify themselves before God by keeping the Law of Moses:
"Israel, pursuing a law of righteousness did not arrive at that law. Why? Because they did not pursue it by faith but as though it were by works.......I testify about them that they have a zeal for God but not in accordance with knowledge. For not knowing about God's righteousness and seeking to establish their own they did not subject themselves to the righteousness of God. For Christ is the end of the law for righteousness to everyone who believes" (Rom9:31- 10:4)
But the principle holds for any of us who seek to be justified before God by our own means without reference to Christ (Eph2:8,9; Titus3:4-6). There are plenty today for example who believe they will be found acceptable to God for the "good life" they have lived despite the fact they never took Jesus seriously.
James on the other hand has an entirely different problem in mind. His concern is people who go to the other extreme and want to rely entirely on their faith in Christ's sacrifice to justify them while they sit back and basically do nothing:
"What use it my brethren if someone says he has faith but he has no works? Can that faith save him?" (Jas2:14)
"You believe that God is one. You do well - the demons also believe and shudder. But are you willing to recognize you foolish fellow that faith without works is useless?" (Jas2:19-20)
So, as we would expect from God's word, there is no contradiction here at all.
James would of course agree with Paul that you can't "earn" your salvation by your own merits independent of Christ. Thats why he also urges his readers to "hold their faith in our glorious Lord Jesus Christ....." (Jas2:1) for example.
And Paul would certainly agree with James that a faith which is "words only" will not save. Thats why he also urges his readers to "be careful to engage in good deeds" (Titus3:8) and to "work out their salvation" (Phil2:12) and that he was mindful of their "work of faith" (1Thess1:3) and that what's important is "faith working through love" (Gal5:6) and so on.
What both would certainly DISAGREE with is the widespread teaching today that our salvation has NOTHING to do with our works, that we are justified by "faith alone" regardless of what we do.