Since we are entirely sinful, and unable to save ourselves, we are entirely dependent upon God for salvation. Salvation is worked by God from beginning to end, and is given as a free gift. Salvation thus has its origin in God and not in us, and is only the result of God's grace (unmerited favour). It is "by grace alone". This teaching is also known as The Five Points of Calvinism, which are best remembered with the acronym TULIP.
Total Depravity. We all are conceived and born in sin. By nature, you are totally incapable of doing any true good, and rather are inclined to do all evil. Your natural spiritual condition is thus much worse than just being sick. You are unable even to believe, and can thus be said to be spiritually dead. (Gen 6:5; Ps 51:5; Jer 13:23; Rom 5:12; Eph 2:1-3).
Unconditional Election. God, out of mere grace, has chosen from the whole human race a certain number of persons to be saved in Christ. This choice was not based on who might later believe and have faith, but was entirely based on God's good pleasure (Acts 13:48; Rom 9:15; Eph 1:4).
Limited Atonement. Christ did not redeem all men by his death. The only ones who were atoned and saved by His death are God's people, the believers elected to salvation. By His death on the cross, Christ obtained eternal salvation for all God's people, and these only (Matt 1:21; John 10:15; 17:9).
Invincible Grace. Man is in himself unable to believe in God. But God works in man's heart by His Holy Spirit, working faith and repentance. The Holy Spirit thus changes man, making him turn away from sin and towards God. Although the grace of the Spirit can be opposed, it can never be resisted completely, and God's Spirit can soften the hardest of hearts (Ezek 36:26; John 6:44; 10:27; Eph 2:8; Php 2:13).
Perseverance of the Saints. Because of the power of sin, believers could not persevere in faith if they were left on their own. But God preserves and keeps all true believers in whom He works faith unto the very end. Those who are elect and in whom God works by His Spirit, can never fall away from God completely, and lose their salvation (John 6:39; 10:28; Rom 8:28-30; Php 1:6).