The Three Most Essential Teachings
Deity and Life of Jesus
The lord Yeshua (Jesus) the Messiah (Christ) is both the son of God and is God. He came in the flesh and dwelt among mankind as a man. Being born of a virgin by the power of the Holy Spirit [Matthew 1:18], he lived a sinless life, and died as a sinner in our place so that we could have eternal life [John 3:14-15]. He spent three days and three nights in the grave [Matthew 12:40], and then God raised him to life on the third day. Forty days later, he ascended to Heaven [Acts 1:1-3] to sit at the right hand of the Father.
Anyone who denies that Jesus is the son of God [1 John 4:15], or denies that he came in the flesh [1 John 4:2-3], or denies that he is the messiah [1 John 2:22] is not from God. Such people are false teachers.
Salvation by Faith
Neither prayer, nor repentance, nor baptism, nor keeping God's commands is capable of saving us from condemnation on Judgement Day (though all are important to the faith in some way), for in breaking God's commands, one is condemned. God does not listen to the prayers of the sinner [Isaiah 1:15]. Repentance is remorse over the fact that you have sinned and is therefore not able to save. Baptism is the symbol of us dying to sin and being raised in Christ Jesus our Lord [Colossians 2:12]. And God's Law demands that those who transgress it are punished. Only by believing in Jesus can one have their sins atoned for and be saved.
Obedience from Faith
True, biblical faith results in obedience to the one you believe in [Romans 1:5, Romans 16:26]. And obedience is the proof of your faith [James 2:14-26]. Those who believe in Jesus obey his commands and put his teachings into practice. Those who believe in God keep his Law. Believing in Jesus means believing in the one who sent him [John 12:44]. Likewise, believing in God means believing in the one whom he sent. Those who claim to believe in Jesus but reject God's Law also rejects Jesus by what they do [Titus 1:16], for Jesus is the Word of God [1 John 1:1-14]. Those who claim that obedience is by definition salvation by works are heretics!
Statement of Faith
The Bible is the final authority in all matters including history and science. But this authority stands or falls with the authority of God's Law. If the Law of God is no longer applicable or no longer has any authority in our lives, then the rest of Scripture is also void of authority except as just another historical document like any other. The one who says, "God's Law no longer applies" might as well say, "the Bible is of no value to us". But if God's Law is still applicable and still has authority, then the Bible is so much more than just another historical document. Furthermore, the authority of the Bible is fully-dependent on Genesis being the truthful historical account of the origin and history of the Earth, and everything in, on, and around it!
All things (including the Bible) must be tested as per God's commands in Deuteronomy 13 and Deuteronomy 18, so that we may know the Truth. Forbidding anything from being tested, including the contents of the Bible, shows that the one who forbids the test is either afraid of, or is hiding, the truth. It is better to test something and come to the wrong conclusion than it is to blindly believe the truth. For one cannot know what the truth is without testing what he or she believes is the truth. The Bible is validated by its unmatched historical and scientific accuracy, it's unmatched internal consistency, and it's perfect prophetic record.
Jesus is the living Word of God and therefore cannot do away with or otherwise nullify God's Law, which is the written Word of God. Rather, Jesus is the authority on how the written Word is to be interpreted. Jesus' interpretation of God's commandments is the original intent of the commandments in question. Likewise, the writings of the prophets (who spoke exactly what God commanded them to speak [Deuteronomy 18:18]) are authoritative in the correct application and interpretation of God's commandments. All prophecies recorded in Scripture (except where Scripture states a specific prophesy to be false) come directly from God and are validated according to the Deuteronomy 13 and Deuteronomy 18 tests. Jesus, likewise, is validated by those same tests, and also through the fulfillment of all of the prophecies made concerning him on his first coming.
God's Law, and only God's Law, defines what is right and wrong, what is sinful and what is not. If anyone claims that something is sinful, they must prove that it is contrary to God's Law. Otherwise, they are guilty of adding to God's commandments [Deuteronomy 12:32]. Likewise, if anyone claims that something is not sinful, they must prove that it is not contrary to God's Law. Otherwise, they are guilty of subtracting from God's commandments [Deuteronomy 12:32]. If anything is claimed to be sinful or not sinful, but the claim is backed-up only by passages outside of God's Law, the person making the claim proves that he or she misunderstands the passage in question.
Salvation comes through faith in Jesus, not by the merits of one's own works. By our works we are condemned, but by our faith we are saved. That said, the one who rebels against God's commandments (God's Law) is condemned and cannot be saved unless they repent of their rebellion. For there is no atonement for deliberate sins. All manner of unintentional sins will be forgiven for the one who believes in Jesus. But the one who knows of, or learns of their sin, yet deliberately continues in those sins will not be forgiven [Hebrews 10:26], even if they claim to believe in Jesus. Those who refuse to keep God's Law live in idolatry. Those who keep God's Law serve God.
There are two forms of salvation. The first is salvation from our sins and from our sinful nature. The second is salvation from death in the lack of fire. Salvation from our sins means forgiveness of sins, which is the destruction of the record of our past sins. It also means being set free from sin, so that we are no longer slaves to sin. Salvation from our sinful nature means we no longer want to live contrary to God's commandments, but instead naturally keep his commandments. The first form of salvation comes immediately to those who believe in Jesus. The second form of salvation will be realized on Judgement Day, when all will be raised from the dead to give an account for everything they have done. The righteous will be granted eternal life and will be spared from the lake of fire. But the wicked will be cast into the lake of fire and die the second death [Revelation 20:14]. The second form of salvation is reserved for those who persist in their faith until death.
Salvation and righteousness are related, but separate issues. While both come by faith in Jesus, righteousness is defined as obedience to God's Law [Romans 2:13]. And only the righteous will be saved on Judgement Day, as already mentioned several times. Righteousness by faith comes from (a) the fact that through faith in Jesus, no sin counts against us, and (b) our faith driving us to naturally obey God's commandments. Natural obedience to God's commandments is the very definition of loving God with all our heart. This includes natural obedience in the One whom he sent. We do not obey to be saved, we obey because we're saved.
A person who ceases to believe in Jesus no longer has forgiveness for any of their future sins and thus forfeits their salvation. Likewise for the person who stops desiring to live according to God's Will and instead starts living according to the sinful desires of the flesh. Such people were once saved, but now are not, but may still be saved again. The teaching that those who leave the faith were never saved in the first place makes God out to be a liar. It is impossible for one to lose their salvation by committing sin by accident.
A complete list of biblical teachings is available through the link provided. There is also a list of false teachings that are refuted by Scripture. See also False Scriptures for passages that have been added to and/or modified from the original, Twisted Scriptures for passages that are twisted to support unbiblical teachings or traditions, and Mistranslated Scriptures for passages that are commonly mistranslated and what the correct translation(s) would be.