The best place to go for the Lutheran view of baptism is Martin Luther himself. His Small Catechism gives a brief yet profound explanation:

What is Baptism?
Baptism is not just plain water, but it is the water included in God's command and combined with God's word.

Which is that word of God?
Christ our Lord says in the last chapter of Matthew: "Therefore, go and make disciples of all nations baptizing them in the name of the Father, and of the Son, and of the Holy Spirit."

What benefits does Baptism give?
It works forgiveness of sins, rescues from death and the devil, and gives eternal salvation to all who believe this, as the words and promises of God declare.

Which are these words and promises of God?
Christ our Lord says in the last chapter of Mark: "Whoever believes and is baptized will be saved, but whoever does not believe will be condemned."

How can water do such great things?
Certainly not just water, but the word of God in and with the water does these things, along with the faith which trusts this word of God in the water. For without God's word the water is plain water and no Baptism. But with the word of God it is a Baptism, that is, a life giving water, rich in grace, and a washing of the new birth in the Holy Spirit, as St. Paul says in Titus chapter three:
"He saved us through the washing of rebirth and renewal by the Holy Spirit, whom He poured out on us generously through Jesus Christ our Savior, so that, having been justified by His grace, we might become heirs having the hope of eternal life. This is a trustworthy saying." (Titus 3:5-8)

What does such baptizing with water indicate?
It indicates that the Old Adam in us should by daily contrition and repentance be drowned and die with all sins and evil desires, and that a new man should daily emerge and arise to live before God in righteousness and purity forever.

Where is this written?
St. Paul writes in Romans chapter six: "We were therefore buried with Him through baptism into death in order that, just as Christ was raised from the dead through the glory of the Father, we too may live a new life." (Romans 6:4)

What we believe about baptism:

Baptism is essentially a means by which He has chosen to bring us His Spirit and the forgiveness of sins. God often uses things which seem ordinary to do miraculous works. He speaks to us through a book. He came to us in human flesh. He even spoke through an ass! God often hides Himself in ordinary elements as He reveals Himself. This is the same with the water of baptism.
We believe in baptismal regeneration. This means that the Spirit has chosen to work through baptismal water in the same way that He works through His word. Reformed Christians often say that the preached word is a means of regeneration but baptism is not. We believe that both are means which God uses to bring His promise to us. Baptism is the gospel in visible form, thus it gives all of the benefits of the gospel.
We believe in infant baptism. Since infants cannot understand the word, God uses baptism as a means to regenerate them and bring them into the faith. Through it, God gives faith. If faith is truly a gift of God and not a human work, God can certainly do this for an infant. He can also do it through whatever means He has chosen.
We believe that baptism is a form of the gospel, not a form of the law. Baptism is an act performed by Christ, through the hands of the administer of the sacrament. It is His gift of life and salvation. It is not a work we do. It is not something we do to profess our faith, or to profess that we will raise our children in the faith. It is a gift of grace through the promise of the gospel.

What we do not believe:

We do not believe that baptism is absolutely necessary for salvation. Since God works through both word and sacrament, the word is sufficient to regenerate and save. However, if one refuses to get baptized, this is evidence that he was never saved since he is denying what Christ has commanded.
We do not believe the Roman Catholic view of baptism. The Roman Catholic church denies that faith is necessarily given at baptism. They also deny that sin remains after baptism.
We do not believe that everyone who was ever baptized will be saved. If one rejects God's offer through baptism, or does not continue in the faith given at baptism, his baptism becomes a means of judgement rather than salvation.
This does not mean that we deny justification by faith alone because we believe baptism saves. The issue is that baptism and faith are not separate things. Baptism gives and strengthens faith. Baptism also delivers the promise which faith clings to.

These are the main points of the Lutheran view of baptism and how it differs from both the Reformed and Roman Catholic teachings on the subject.

"...It is the holy bath of regeneration through the Holy Spirit [Titus 3: 5], in which we bathe and with which we are washed of sin and death by the Holy Spirit, as in the innocent holy blood of the Lamb of God."
Martin Luther (LW 41: 151)

1. Holy Baptism is an initiation and adoption into the Body of Christ.
2. Holy Baptism is in the Name of the Father, Son, and Holy Spirit. As a                              remembrance of Baptism, one may make the sign of the cross whenever the                          Name is spoken. See "Morning Prayer" and "Evening Prayer." (CLC p. 344)
3. Celebrate the day of your baptism as you would your birthday.
4. Read and reflect on Luther's Small Catechism (CLC p. 339-340) and Large Catechism (CLC pp. 423-431) on Holy Baptism.
5. Holy Baptism precedes Holy Communion as birth precedes eating.
6. Read and reflect on scripture passages regarding Baptism. For example:
Matthew 28:19-20 (ESV)
Go therefore and make disciples of all nations, baptizing them in[a] the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.”
Mark 16:16 (ESV)
Whoever believes and is baptized will be saved, but whoever does not believe will be condemned.
Acts 2:37-41 (ESV)
Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, “Brothers, what shall we do?” And Peter said to them, “Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit. For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself.” And with many other words he bore witness and continued to exhort them, saying, “Save yourselves from this crooked generation.” So those who received his word were baptized, and there were added that day about three thousand souls.

Acts 8:26-38 (ESV)
Philip and the Ethiopian Eunuch
Now an angel of the Lord said to Philip, “Rise and go toward the south[a] to the road that goes down from Jerusalem to Gaza.” This is a desert place. And he rose and went. And there was an Ethiopian, a eunuch, a court official of Candace, queen of the Ethiopians, who was in charge of all her treasure. He had come to Jerusalem to worship and was returning, seated in his chariot, and he was reading the prophet Isaiah. And the Spirit said to Philip, “Go over and join this chariot.” So Philip ran to him and heard him reading Isaiah the prophet and asked, “Do you understand what you are reading?” And he said, “How can I, unless someone guides me?” And he invited Philip to come up and sit with him. Now the passage of the Scripture that he was reading was this:

“Like a sheep he was led to the slaughter
and like a lamb before its shearer is silent,
so he opens not his mouth.

in his humiliation justice was denied him.
Who can describe his generation?
For his life is taken away from the earth.”

And the eunuch said to Philip, “About whom, I ask you, does the prophet say this, about himself or about someone else?” Then Philip opened his mouth, and beginning with this Scripture he told him the good news about Jesus. And as they were going along the road they came to some water, and the eunuch said, “See, here is water! What prevents me from being baptized?” And he commanded the chariot to stop, and they both went down into the water, Philip and the eunuch, and he baptized him.

From THE GUIDE  Seven Mark Society Second Edition

Page references are from CONCORDIA The Lutheran Confessions Concordia Publishing House Second Addition, Copyright 2005,2006 (CLC)

The Defense of the Augsburg Confession

Article IX: Of Baptism.
51] The Ninth Article has been approved, in which we confess that Baptism is necessary to salvation, and that children are to be baptized, and that the baptism of children is not in vain, but is necessary and effectual to salvation. 52] And since the Gospel is taught among us purely and diligently, by God's favor we receive also from it this fruit, that in our Churches no Anabaptists have arisen [have not gained ground in our Churches], because the people have been fortified by God's Word against the wicked and seditious faction of these robbers. And as we condemn quite a number of other errors of the Anabaptists, we condemn this also, that they dispute that the baptism of little children is profitable. For it is very certain that the promise of salvation pertains also to little children [that the divine promises of grace and of the Holy Ghost belong not alone to the old, but also to children]. It does not, however, pertain to those who are outside of Christ's Church, where there is neither Word nor Sacraments, because the kingdom of Christ exists only with the Word and Sacraments. Therefore it is necessary to baptize little children, that the promise of salvation may be applied to them, according to Christ's command, Matt. 28:19: Baptize all nations. Just as here salvation is offered to all, so Baptism is offered to all, to men, women, children, infants. It clearly follows, therefore, that infants are to be baptized, because with Baptism salvation [the universal grace and treasure of the Gospel] is offered. 53] Secondly, it is manifest that God approves of the baptism of little children. Therefore the Anabaptists, who condemn the baptism of little children, believe wickedly. That God, however, approves of the baptism of little children is shown by this, namely, that God gives the Holy Ghost to those thus baptized [to many who have been baptized in childhood]. For if this baptism would be in vain, the Holy Ghost would be given to none, none would be saved, and finally there would be no Church. [For there have been many holy men in the Church who have not been baptized otherwise.] This reason, even taken alone, can sufficiently establish good and godly minds against the godless and fanatical opinions of the Anabaptists.

The Second Mark:  Holy Baptism