This is a subject of much debate. Generally, however, it is accepted that there are three major components of a saving faith.
Notitia refers to the fact that we have the correct knowledge or content. Today people often claim that sincerity in one’s faith is the most important aspect. Sincerity may be important, but it is not all important. What you believe has to be right. You may sincerely believe in reincarnation, but that is not part of a saving faith, but rather part of a damning faith. Being sincerely wrong is no virtue.
It does not mean you need a comprehensive knowledge (if so, we all would be lost), but there is some (undefined) minimum set of correct beliefs you must hold, such as the fact the God exists.
AssensusAssensus means that you not only have the notitia (content) but you also give intellectual assent to the content. This is a non-volitional agreement; you cannot will yourself or make a decision to believe. There may be a process by which you can ultimately reach a point where you can honestly affirm a proposition, either through education or divine intervention, but you cannot simply tell yourself I will believe.
James famously refers to demons in his epistle:
You believe that God is one. You do well; the demons also believe, and shudder. (James 2:19, NASB)The demons have both notitia (correct content) and assensus (intellectual assent), but their faith was/is not a saving faith. It lacks the third component fiducia. (Although even if they had it, it is not clear they would be saved. Nowhere is it mentioned that there exists a redemptive plan for fallen angels.)
FiduciaThis is the complex “of the heart” faith, as opposed to the cerebral notitia and assensus. This relates to our conviction and passion. This is our conscience. This is the part of faith that goes beyond knowing that the bible teaches us not to steal, and acknowledging that stealing is a sin, to being convicted by the Holy Spirit that stealing is wrong.
With fiducia, we not only know the content of the gospel and believe it to be true, we also believe it to be good. This is clearly, in its entirety, a gift of God. Before regeneration, we are dead in sin and cannot seek or please God. After the gift of faith, we are radically violated. We now (imperfectly) seek God. Our biblical knowledge is buttressed by conviction that God is good, and the things of God are greatly to be desired.