"Faith is a steady and certain knowledge of the Divine benevolence towards us, which, being founded on the truth of the gratuitous promise in Christ, is both revealed to our minds, and confirmed to our hearts, by the Holy Spirit.” - John Calvin
Faith is believing that God will keep His promises, despite circumstances that seem to be to the contrary! ... Faith takes God at His Word, even when all in the world currently seems contrary to his purposes. Faith is resting one's heart and mind on God's immutable, trustworthy character and sees the eternal in the present and choose to live accordingly, in dependence on the power of the Holy Spirit. And importantly, faith relies on what Christ has done for us as opposed to our own efforts.
Louis Berkhof defines genuine faith including an intellectual element (notitia), which is "a positive recognition of the truth”; an emotional element (assensus), which includes “a deep conviction of the truth”; and a volitional element (fiducia), which involves “a personal trust in Christ as Savior and Lord, including a surrender … to Christ.” (Louis Berkhof, Systematic Theology. Grand Rapids: Eerdmans, 1939)
"Saving faith is not a native product of the human heart, but is a spiritual grace communicated from on High." - A.W. Pink
"It is not faith that saves, but faith in Jesus Christ.... It is not, strictly speaking, even faith in Christ that saves, but Christ that saves through faith. The saving power resides exclusively, not in the act of faith or the attitude of faith or in the nature of faith, but in the object of faith." - B. B. Warfield
"Faith is the principal work of the Holy Spirit." - Calvin (Institutes 3.1.4).
"Faith is the proper and entire work of the Holy Spirit." - Calvin (Institutes 3.1.4).
"We cannot quicken faith in ourselves or predispose ourselves for it in any way. There is not in us any commencement of faith or any preparation of it." - John Calvin,Commentary John 6:45
Related: Sola Fide, Justification