"Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction: for all have sinned and fall short of the glory of God, and are justified by his grace as a gift, through the redemption that is in Christ Jesus, whom God put forward as a propitiation by his blood, to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins. It was to show his righteousness at the present time, so that he might be just and the justifier of the one who has faith in Jesus."
Bridges goes on to write:
This then is the gospel with which we need to become thoroughly familiar and that we need to preach to ourselves every day. Jesus by His death and shed blood completely satisfied the justice of God and the claims of His broken law. By His perfect obedience He positively fulfilled the requirements of the law. Thus in both its precepts and penalty, the law of God in its most exacting requirements was fulfilled in Jesus. And He did this in our place as our representative and our substitute.
To preach the gospel to yourself, then, means that you continually face up to your own sinfulness and then flee to Jesus through faith in His shed blood and righteous life. It means that you appropriate, again by faith, the fact that Jesus fully satisfied the law of God, that He is your propitiation, and that God's holy wrath is no longer directed toward you.
To preach the gospel to yourself means that you take at face value the precious words of Romans 4:7-8:
"Blessed are they whose trangressions are forgiven, whose sins are covered. Blessed is the man whose sin the Lord will never count against him."
It means that you believe in the testimony of God that "Therefore, there is now no condemnation for those who are in Christ Jesus." (Romans 8:1). It means you believe that "Christ redeemed [you] from the curse of the law by becoming a curse for [you], for it is written: 'Cursed is everyone who is hung on a tree'" (Galatians 3:13). It means you believe He forgave you all your sins (Colossians 2:13) and now "[presents you] holy in his sight, without blemish and free from accusation" (Colossians 1:22).
Turning to the Old Testament to preach the gospel to yourself means that you appropriate by faith the words of Isaiah 53:6:
"We all, like sheep, have gone astray, each of us has turned to his own way; and the Lord has laid on him the iniquity of us all."
It means that you dwell upon the promise that God has removed your transgressions from you as far as the east is from the west (Psalm 103:12), that He has blotted out your transgressions and remembers your sin no more (Isaiah 43:25). But it means you realize that all these wonderful promises of forgiveness are based upon the atoning death of Jesus Christ.- Jerry Bridges, The Discipline of Grace (NavPress, 2004), pp 58-60.