Short answer
You become a Muslim by saying, and meaning, that there is no god but Allah (﷾) and that Muhammad (ﷺ) is the Messenger of Allah (﷾). You say it knowing what it means. This is called the Shahadah, the first of Islam's five pillars. It costs nothing, and it needs no priest and no waiting period. It is the doorway into a complete way of life, which a new Muslim learns step by step. Islam teaches that entering it wipes out all past sins. A man once held back, afraid of what he had done. The Prophet (ﷺ) told him that Islam wipes out everything before it. The Qur'an tells all who have wronged themselves not to lose hope in Allah's (﷾) mercy. A Christian who becomes Muslim does not leave Jesus behind. He keeps the faith Jesus taught: worship of the one true God (﷾), and belief in the messengers God (﷾) sent.
Full explanation
The words that make a person Muslim
The Qur'an says: know that there is no god but Allah (﷾). The Prophet (ﷺ) named the two-part testimony as the first of the five things on which Islam is built. He sent Mu'adh, one of his companions, to a land with People of the Book, meaning Jews and Christians. He told Mu'adh to call them first to this testimony, and only then to teach them prayer and charity. He also said that whoever dies knowing there is no god but Allah (﷾) will enter Paradise. So a person says the words knowing what they mean, and says them from the heart. The page "The shahada" on this site gives the words and what comes next.
“Know, therefore, that there is no god but Allah, and ask forgiveness for thy fault, and for the men and women who believe: for Allah knows how ye move about and how ye dwell in your homes.”
Ibn Umar reports that the Prophet (ﷺ) said Islam is built on five: to bear witness that there is no god but Allah and that Muhammad is the Messenger of Allah, to establish the prayer, to pay zakah, to perform the pilgrimage, and to fast the month of Ramadan.
Ibn Abbas reports, through his freed slave Abu Ma'bad, that when the Prophet (ﷺ) sent Mu'adh to Yemen, he told him he was going to a people of the Scripture. He was to invite them first to testify that there is no god but Allah and that Muhammad is His Messenger. Only if they accepted that was he to teach them the five daily prayers, and then the zakah (the obligatory charity).
Uthman reports that the Prophet (ﷺ) said whoever dies knowing that there is no god but Allah will enter Paradise.
Nothing to pay and no one in between
Islam has no priesthood and no fee. There is no rite that a person must wait for. The Qur'an says God (﷾) is near and answers the one who calls on Him. It says He is nearer to a person than the vein in his own neck. Many new Muslims say the words in front of other Muslims, so that they can be welcomed. But the Qur'an puts no one between a person and God (﷾).
“When My servants ask thee concerning Me, I am indeed close (to them): I listen to the prayer of every suppliant when he calleth on Me: Let them also, with a will, Listen to My call, and believe in Me: That they may walk in the right way.”
“It was We Who created man, and We know what dark suggestions his soul makes to him: for We are nearer to him than (his) jugular vein.”
The past is wiped clean
Amr ibn al-As came to the Prophet (ﷺ) to accept Islam, then drew back his hand. He wanted to be sure he would be forgiven. The Prophet (ﷺ) asked him if he did not know that Islam wipes out everything that came before it. The Qur'an tells all who have wronged themselves not to lose hope in Allah's (﷾) mercy. It promises that God (﷾) turns the evil deeds of one who repents, believes and does good into good. The Prophet (ﷺ) also said that whoever holds to the testimony until death will in the end enter Paradise, even after grave sins.
Amr ibn al-As, near death, said that before Islam no one was more hateful to him than the Prophet (ﷺ), and he had wished to kill him. He told how he came to the Prophet to accept Islam. He asked the Prophet to stretch out his right hand so he could pledge, then drew his own hand back. Asked why, he said he wanted a condition: that he be forgiven. The Prophet asked whether he did not know that Islam wipes out everything that came before it.
“Say: "O my Servants who have transgressed against their souls! Despair not of the Mercy of Allah: for Allah forgives all sins: for He is Oft-Forgiving, Most Merciful.”
“Unless he repents, believes, and works righteous deeds, for Allah will change the evil of such persons into good, and Allah is Oft-Forgiving, Most Merciful,”
Abu Dharr reports that the Prophet (ﷺ) said Gabriel brought him the good news that whoever of his community dies without associating anything with Allah will enter Paradise. Abu Dharr asked: even if he committed adultery and theft? The Prophet said: even if he committed adultery and theft.
Abu Dharr reports that the Prophet (ﷺ) said that anyone who says there is no god but Allah, and dies holding to it, will enter Paradise. Abu Dharr asked: even if he had committed adultery and theft? The Prophet said: even so, and repeated it each time Abu Dharr asked again. Al-Bukhari adds that this concerns the one who, at death or before it, repents and says there is no god but Allah: he is forgiven.
Christians who recognised the truth
The Qur'an describes Christians as the nearest in love to the believers. It describes some of them listening to the revelation brought by the Messenger (ﷺ). Their eyes overflowed with tears because they recognised the truth. They asked God (﷾) to write them among the witnesses.
“nearest among them in love to the believers wilt thou find those who say, "We are Christians": because amongst these are men devoted to learning and men who have renounced the world, and they are not arrogant.”
“And when they listen to the revelation received by the Messenger, thou wilt see their eyes overflowing with tears, for they recognise the truth: they pray: "Our Lord! we believe; write us down among the witnesses.”
Following Jesus, not leaving him
In the New Testament Gospels, Jesus calls the first commandment the oneness of God (﷾). He also speaks of the only true God (﷾) and of the one God (﷾) sent. That is the shape of the Shahadah: the one God (﷾), and a messenger He sent. In the Qur'an the disciples of Jesus ask him to bear witness that they are Muslims. In the Qur'an Jesus also gives good news of a messenger to come after him. A Christian who becomes Muslim keeps his love for Jesus and follows the message Jesus brought.
“And Jesus answered him, The first of all the commandments is, Hear, O Israel; The Lord our God is one Lord:”
“And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent.”
“When Jesus found Unbelief on their part He said: "Who will be My helpers to (the work of) Allah?" Said the disciples: "We are Allah's helpers: We believe in Allah, and do thou bear witness that we are Muslims.”
“And remember, Jesus, the son of Mary, said: "O Children of Israel! I am the messenger of Allah (sent) to you, confirming the Law (which came) before me, and giving Glad Tidings of a Messenger to come after me, whose name shall be Ahmad." But when he came to them with Clear Signs, they said, "this is evident sorcery!"”
The invitation to common terms
The Qur'an calls Jews and Christians to common terms. They are to worship none but God (﷾), to set up no partners with Him, and to take no one as lord besides Him.
“Say: "O People of the Book! come to common terms as between us and you: That we worship none but Allah; that we associate no partners with him; that we erect not, from among ourselves, Lords and patrons other than Allah." If then they turn back, say ye: "Bear witness that we (at least) are Muslims (bowing to Allah's Will).”
Becoming Muslim
- There is nothing to pay, no priest to find and no ceremony to wait for.
- Believe it and say it, knowingly and sincerely: there is no god but Allah (﷾), and Muhammad (ﷺ) is the Messenger of Allah (﷾).
- Your past is wiped clean: Islam wipes out everything that came before it.
- Never lose hope in Allah's (﷾) mercy: He forgives all sins.
- You do not leave Jesus behind. You keep your love for him, and follow the message he brought: the worship of the one true God (﷾).
Perspectives
The Islamic perspective
A person becomes Muslim by a declaration, made with knowledge and sincerity. It is that there is no god but Allah (﷾) and that Muhammad (ﷺ) is His Messenger. Nothing else is needed to enter Islam. And entering it wipes out the sins that came before.
The first of Islam's five pillars is the testimony. It is that there is no god but Allah (﷾) and that Muhammad (ﷺ) is the Messenger of Allah (﷾).
The Prophet (ﷺ) told his envoy to call People of the Book first to this testimony. Prayer and charity were to be taught after it.
The testimony must be made with knowledge of what it means.
The Qur'an places no priest or officiant between a person and God (﷾).
Accepting Islam wipes out the sins that came before it.
The Qur'an tells those who have wronged themselves not to despair of Allah's (﷾) mercy, for He forgives all sins.
The Qur'an describes Christians who wept on hearing the revelation because they recognised the truth.
The Qur'an records the disciples of Jesus calling themselves Muslims.