The Qur'an states that Jews and Christians both worship the one true God. That Abraham worshiped Allah (simply the word in Arabic for God.) That the God that Muslims pray to is the same God that was revealed to Abraham, Isaac, Ishmael, and the Children of Israel. That Moses and Jesus were prophets from this same God. That all are the same under the eyes of God, that Muslims, Christians, and Jews bow down in prayer to Allah. That their belief places them on the right path towards God. That there is no need to dispute with Christians and Jews, for all worship the same Lord; that one should simply be tolerant of the beliefs of the other and take responsibility for ones own actions.
The Qur'an also teaches that Jews and Christians have no reason to dispute with one another. The Qur'an harshly criticizes those that attack the religion of the other. This is because both religions have received a divine revelation, a holy scripture that Muslims also believe in. That only God can judge between one and the other when the End of Time comes. Muslims are advised to simply focus on what these three religions have in common in order to make peace. As the Qur'an says:
Say: “O People of the Book! Come to what is common between us and you: That we worship none but God, that we associate no partners with Him, that we erect not, from among ourselves, Lords other than Allah. If then they turn back, say: 'Bear witness that we are bowing to Allah’s will.'"
That is, to simply accept that Jews, Christians, and Muslims believe in the one true God, worship no other God but Allah, and that all reject idolatry. The Qur'an teaches to avoid futile disputes, and to testify of one's faith through example. Muslims do not seek to convert others, but have traditionally done so through example, by living a life of virtue and submitting oneself to God's will.