Fundamental to that topic is that "The spiritual man makes judgments about all things" 1Co 2:15 The Bereans were commended for even scrutinizing Paul's teachings. "Now the Bereans were of more noble character than the Thessalonians, for they received the message with great eagerness and examined the Scriptures every day to see if what Paul said was true." Acts 17:11
One of the most misconstrued verses people use to discourage practicing discernment is found in the Sermon on the Mount where Jesus said, "Judge not, that you be not judged." Mt 7:1 He was using a proverbial form of speech, as he does much in that sermon, reflective of the rhetoric of Proverbs, but here speaking of the principle that if you judge others, they will judge you. It's human nature. Try it. He himself judged others and even told his enemies, "Stop judging by mere appearances, and make a right judgment." John 7:24 And guess what? They judged him. Don't be intimidated in practicing discernment. But make sure you get it right.
As for principles of discernment, the basic idea is to scrutinize all ideas in light of scripture and in light of the Spirit. John writes, "We are from God, and whoever knows God listens to us; but whoever is not from God does not listen to us. This is how we recognize the Spirit of truth and the spirit of falsehood." 1John 4:6 Can people hear what the apostles are teaching? Are they blind to it? Do they "get it"? Or even if they understand, do they discard it? To discern false teaching you must be familiar with correct teaching. So those practicing discernment should be heavily involved with personal Bible study.
Understanding scripture is not purely a function of academic study. There's a spiritual element to understanding, an intuitive element, as Paul says in 1Cor 2:6-16 "We do, however, speak a message of wisdom among the mature, but not the wisdom of this age or of the rulers of this age, who are coming to nothing. No, we speak of God’s secret wisdom, a wisdom that has been hidden and that God destined for our glory before time began. None of the rulers of this age understood it, for if they had, they would not have crucified the Lord of glory. However, as it is written: "No eye has seen, no ear has heard, no mind has conceived what God has prepared for those who love him" — but God has revealed it to us by his Spirit. The Spirit searches all things, even the deep things of God. For who among men knows the thoughts of a man except the man’s spirit within him? In the same way no one knows the thoughts of God except the Spirit of God. We have not received the spirit of the world but the Spirit who is from God, that we may understand what God has freely given us. This is what we speak, not in words taught us by human wisdom but in words taught by the Spirit, expressing spiritual truths in spiritual words. The man without the Spirit does not accept the things that come from the Spirit of God, for they are foolishness to him, and he cannot understand them, because they are spiritually discerned. The spiritual man makes judgments about all things, but he himself is not subject to any man’s judgment: "For who has known the mind of the Lord that he may instruct him?" But we have the mind of Christ."