The means of grace is simply the doctrine of imputed righteousness put into action.
Man, in his natural state, is completely sinful and hostile to God (
Romans 8:7) in the flesh, there is nothing good in him (
Romans 7:18). Therefore, God always comes to us from outside ourselves (
extra nos).
Those who hold to infused or imparted righteousness (RCC and Pentecostals, among others) believe that since man is not completely degenerate, that in our own power the unregenerate are able to reach out to God and assist him in bringing ourselves to righteousness in Christ (synergism), either through works or conscious decisions or sincere desires.
The doctrine of imputed righteousness dictates that God, acting completely alone, "puts righteousness in" us, or declares us totally righteous, for the sake of the completely sufficient, atoning sacrifice of Christ.
God acts through his holy Word, as he did when he spoke the universe into existence and when he called Lazarus forth from the dead. He creates and gives life through his Word. This same Word is active when God promises to save us or to forgive our sins (and there is no forgiveness of sins outside of salvation.) Because of the promises of God given to us in Holy Scripture, we know that God's Word is equally active in what we refer to as Word and Sacrament - the means of grace.
No one ever came to faith in Christ apart from the Word coming to him from outside himself, through physical means. What trips up a lot of Evangelicals is that they forget that speaking and reading are entirely physical processes of communication.
Speaking and hearing involves human brains, speech organs, sound waves in air, and hearing organs. All 100% physical. God attaches his spiritual Word to physical speech.
Likewise, communication by reading or sign language involves 100% physical means of communication: paper and ink, hands and faces, light, eyes and brains. All physical.
In the same way that God attaches his spiritual Word to physical means of communication, we know from God's promises in scripture that he attaches his spiritual Word to physical water in Baptism, and through his Word he unites the true body and blood of Christ with the consecrated bread and wine in the Lord's Supper.
We see clear promises in scripture that show that God initially saves us (Justification) through the proclamation of the Word (Law and Gospel), and through Baptism.
We see clear promises in scripture that show that God continues to pour out his forgiveness of sins through the proclamation of the Word (Confession and Absolution), and in Lord's Supper (Sanctification).
Matthew 28:19 Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, 20 teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
Galatians 3:27 For as many of you as were baptized into Christ have put on Christ.
Acts 22:16 And now why do you wait? Rise and be baptized and wash away your sins, calling on his name.’
Romans 6: 3 Do you not know that all of us who have been baptized into Christ Jesus were baptized into his death? 4 We were buried therefore with him by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.
Matthew 26: 26 Now as they were eating, Jesus took bread, and after blessing it broke it and gave it to the disciples, and said, “Take, eat; this is my body.” 27 And he took a cup, and when he had given thanks he gave it to them, saying, “Drink of it, all of you, 28 for this is my blood of the covenant, which is poured out for many for the forgiveness of sins. 29 I tell you I will not drink again of this fruit of the vine until that day when I drink it new with you in my Father's kingdom.”
1 Corinthians 11: 27 Whoever, therefore, eats the bread or drinks the cup of the Lord in an unworthy manner will be guilty concerning the body and blood of the Lord. 28 Let a person examine himself, then, and so eat of the bread and drink of the cup. 29 For anyone who eats and drinks without discerning the body eats and drinks judgment on himself.
(Among other scriptures)
Here are a few links that may be helpful for you as you investigate the means of grace.
The Means of Grace - Part II - Wisconsin Evangelical Lutheran Synod (WELS)
Means of Grace? | The Lutheran Church - Missouri Synod
The Small Catechism - Book of Concord - Baptism
The Large Catechism - Book of Concord - Baptism
The Small Catechism - Book of Concord - Sacrament of the Altar
The Large Catechism - Book of Concord - Sacrament of the Altar
Of the Means of Grace | The Lutheran Church - Missouri Synod
VI. THE MEANS OF GRACE | Wisconsin Evangelical Lutheran Synod (WELS)
The Lutheran Church - Missouri Synod: