The Puritans on the Covenant of Grace

Westminster Confession of Faith, 7.2, 3. The first covenant made with man was a covenant of works. . . . Man by his fall having made himself incapable of life by that covenant, the Lord was pleased to make a second, commonly called the Covenant of Grace; whereby he freely offereth unto sinners life and salvation by Jesus Christ, requiring of them faith in him, that they may be saved. . . .

Westminster Confession of Faith, 7.5. This covenant was differently administered in the time of the law, and in the time of the gospel: under the law it was administered by promises, prophecies, sacrifices, circumcision, the paschal lamb, and other types and ordinances delivered to the people of the Jews, all fore-signifying Christ to come, which were for that time sufficient and efficacious, through the operation of the Spirit, to instruct and build up the elect in faith in the promised Messiah, by whom they had full remission of sins, and eternal salvation; and is called the Old Testament.

The following excerpt is taken from A Puritan Theology: Doctrine for Life; it is the Conclusion of a chapter titled "The Puritans on the Covenant of Grace." 

A basic grasp of the covenant of grace helps students of Reformed theologians in the Puritan tradition to understand their basic approach to interpreting the Bible. From the very entrance of sin into the world, God revealed His plan for redemption (Gen. 3:15). As that revelation is unfolded and enlarged through successive covenants, the plan of God for the salvation of His people becomes ever more clear. In other words, From Genesis to Revelation salvation remains firmly centered on the person and work of Jesus Christ, with the Holy Spirit applying the benefits of Christ's redemptive work to those whom the Father has chosen for everlasting life and given to His Son. The covenant of grace is two-sided (dipleuric) in its administration. salvation is trinitarian, involving the three persons of the Trinity. The Holy Spirit brings sinners into union with Jesus Christ by producing faith in the elect. 

Upon believing and receiving forgiveness of sins, believers are instated into covenant with God and required to live a life of holiness in obedience to His commandments. this was as true for Abraham, Moses, or David as for Peter and the apostles, and the same is true for God's people today. For that reason, the covenant of grace unites the people of God into one family, both Jews and Gentiles, all who are partakers of a gracious salvation that was planned in eternity and realized in time. Saints in the Old Testament looked forward to Christ's coming to accomplish His redemptive work, whereas saints in the New Testament and beyond remember and rejoice in that work as wholly accomplished in His death and resurrection. For that reason, Christ assumes the central place in redemptive history, which is nothing but the unfolding of the mystery of the covenant of grace (Joel R. Beeke and Mark Jones, A Puritan Theology: Doctrine for Life, 278).

Blessings and Benefits

Westminster Confession of Faith, Chapter VII, Section IV--This covenant of grace is frequently set  forth in Scripture by the name of a testament, in reference to the death of Jesus Christ the testator, and to the everlasting inheritance, with all things belonging to it, therein bequeathed.

A. A. Hodge expounds:

Christ as mediatorial King, administers to his people the benefits of his covenant; and by his providence, his Word, and his Spirit, he causes them to become severally recipients of these blessings, according to his will. These benefits he offers to all men in the gospel. He promises to grant them on the condition they are received. In the case of his own people, he works faith in them, and as their Surety engages for them and makes good all that is suspended upon or conveyed through their agency. In the whole sphere of our experience every Christian duty is a Christian grace; for we can fulfill the conditions of repentance and faith only as it is given to us by our Surety. All Christian graces also involve Christian duties. So that Christ at once purchases salvation for us, and applies salvation to us; commands us to do, and works in us to obey; offers us grace and eternal life on conditions, and gives us the conditions and the grace and the eternal life. What he gives us he expects us to exercise. What he demands of us he at once gives us. Viewed on God's side, faith and repentance are gifts of the Son. Viewed on our side, they are duties and gracious experiences, the first symptoms of salvation begun--instruments wherewith further grace may be attained. Viewed in connection with the covenant of grace, they are elements of the promise of the Father to the Son, conditioned upon his mediatorial work. Viewed in relation to salvation, they are indices of its commencement and conditions sine qua non [something that is essential, something that is indispensable] of its completion (A. A. Hodge, The Confession of Faith, 127-128).