Lutherans, Methodists, and Calvinists believe that justification is an event (as opposed to the Roman Catholic church and the Orthodox church who believe it is a process). If justification is an event, when does it happen? Is it at the moment of conversion, at baptism, or at some other time?
According to most independent, fundamentalist Baptists, (and to the best of my knowledge, the groups that you mentioned) justification is a one-time event that happens at the moment of conversion, when a sinner repents on his or her sins and puts their faith in Christ for salvation.
This would be in line with a Calvinist view. Justification is a result of salvation, and is something granted freely as the gift of salvation, apart from any works of man.
The very same Wikipedia article that you linked to outlines the relationship between Justification and Sola Fide, for those denominations that subscribe to the view that salvation is by faith alone.
This article covers more groups independently, rather than lumping protestants entirely into a group, and may provide more clarity on how different denominations view the topic.
Lutherans who hold to their confessions [ http://bookofconcord.org/ ] believe that justification, faith, and baptism go together. A baptized infant believes the Gospel at its baptism. An adult who falls away from faith in Christ which has been given in Baptism and is converted is returning to the promise of the Gospel which has been applied to him in Baptism.
Lutherans believe that faith in Christ is the work of the Holy Spirit alone. Human will is bound and unable to assist with conversion. The Holy Spirit works faith through the external Word--that is, the preached Gospel, the written or read Scriptures.
At the same time, faith worked in Christ by the preached Word leads to Baptism, which is "the washing of regeneration and renewal in the Holy Spirit" (Titus 3). Rather than looking for or to an experience of conversion, Lutherans look to God's works and promises. Rather than looking to his feeling of faith, or his conversion experience, decision, or sanctified life, a Lutheran will look to the forgiveness of sins promised in the Gospel to all sinners on account of Christ's propitiatory death, and he will look to the promise of God in Baptism (as well as absolution, and the sacrament of Christ's body and blood) that Christ's merits have been given to him.
In Luther's sermon on Matthew 8:1-13 in his 1525 "Church Postil" [ http://www.lutherdansk.dk/Web-Fastepostillen%20AM/index.htm ] he talks about the faith of infants in Baptism. Another key writing is the Large Catechism's section on Baptism, where Luther has a section dealing specifically with Anabaptist arguments against infant baptism and infant faith. The Large Catechism can be found at the Book of Concord website linked above.
Some excerpts from the sermon on Matthew I've found helpful:
First we must let the foundation stand firm and sure, that nobody will be saved by the faith or righteousness of another, but only by his own; and on the other hand nobody will be condemned for the unbelief or sins of another, but for his own unbelief; as the Gospel says clearly and distinctly in Mk 16,16: ”He that believeth and is baptized shall be saved; but he that disbelieveth shall be condemned.” And Rom 1, 17: ”The righteous shall live by faith.” And Jn 3, 16-18: ”Whosoever believeth on him should not perish, but have eternal life. He that believeth on him is not judged: he that believeth not hath been judged already.” These are clear, public words, that every one must believe for himself, and nobody can help himself by the faith of others, without his own faith. From these passages we dare not depart and we must not deny them, let them strike where they may, and we ought rather let the world perish than change this divine truth. And if any plausible argument is made against it, that you are not able to refute, you must confess that you do not understand the matter and commit it to God, rather than admit anything contrary to these clear statements. Whatever may become of the heathen, Jews, Turks, little children and everything that exists, these words must be right and true.
Now the question is, what becomes of the young children, seeing that they have not yet reason and are not able to believe for themselves, because it is written in Rom 10, 17: ”Belief cometh of hearing, and hearing by the word of Christ.” Little children neither hear nor understand the Word of God, and therefore they can have no faith of their own.
If now we cannot give a better answer to this question and prove that the little children themselves believe and have their own faith, my sincere counsel and judgment is, that we abstain altogether and the sooner the better, and never baptize a child, so that we may not mock and blaspheme the adorable majesty of God by such trifling and juggling with nothing in it. Therefore we here conclude and declare that in baptism the children themselves believe and have their own faith, which God effects in them through the sponsors, when in the faith of the Christian church they intercede for them and bring them to baptism....
So here we also say, that children are not baptized in the faith of the sponsors or of the church; but the faith of sponsors and of the church prays and gains faith for them, in which they are baptized and believe for themselves. For this we have strong and firm Scripture proof, Mt 19,13-15; Mk 10, 13-16; Lk 18, 15-16. When some brought little children to the Lord Jesus that he should touch them, and the disciples forbade them, he rebuked the disciples, and embraced the children, and laid his hands upon them and blessed them, and said: ”To such belongeth the kingdom of God” etc. These passages nobody will take from us, nor refute with good proof. For here is written: Christ will permit no one to forbid that little children should be brought to him; nay, be bids them to be brought to him, and blesses them and gives to them the kingdom of heaven. Let us give due heed to this Scripture.
This is undoubtedly written of natural children. The interpretation of Christ's words, as if he had meant only spiritual children, who are small in humility, will not stand. For they were small children as to their bodies, which Luke calls infants. His blessing is placed upon these, and of these he says that the kingdom of heaven is theirs. Will we say they were without faith of their own? Then the passages quoted above are untrue: ”He that disbelieveth shall be condemned.” Then Christ also speaks falsely or feigns, when he says the kingdom of heaven is theirs, and is not really speaking of the true kingdom of heaven. Interpret these words of Christ as you please, we have it that children are to be brought to Christ and not to be forbidden to be brought: and when they are brought to Christ, he here compels us to believe that he blesses them and gives to them the kingdom of heaven, as he does with these children. And it is in no way proper for us to act and believe otherwise as long as the words stand: ”Suffer the little children to come unto me, and forbid them not.” Not less is it proper for us to believe that when they are brought to him he embraces them, blesses them, and bestows upon them heaven, as long as the text stands that he blessed the children which were brought to him and gave heaven to them. Who can ignore this text? Who will be so bold as not to suffer little children to come to baptism, or not to believe that Christ blesses them when they come?
In the Methodist tradition, a person is justified when they accept the grace God has given them, and make a decision to follow his will rather than their own.
Though justification by itself is not a process, it is the beginning of the process of sanctification, in which we work with God to transform us into the people God intended us to be. This is, as far as I understand, similar to the Catholic and Orthodox concept of theosis.
Justification, if it is an event, probably happened that weekend when Jesus was crucified, died and was buried.
However, since God exists outside of time, from His perspective there may not be a "moment" when justification happened.
I think the better question is why does it matter when justification happened?