The Bible teaches clearly that there is only one way of salvation.  All people stand under the judgement of God and need his forgiveness.  All are called to repent and believe in Jesus Christ.

Salvation is by the grace of God alone, through faith in Christ alone (cf. Acts 2 v38)

God is holy, man is sinful

The bible teaches that God is a perfect, holy and awsome God (Isaiah 6) who made the world (and universe) perfect (Genesis 1 v31) but Adam (the first man) sinned against God and consequently sin entered into the world and all humanity (Genesis 3 v6, Romans 5 v12). Sin has spread to all the descendants of Adam and therefore all people are under the judgement of God and his righteous wrath burns against them.  Unless a person is reconciled to God they are under His condemnation and His just judgement against them is that they will be separated from Him forever in Hell. (Romans 1 v18, 2 v16, Revelation 20 v15)

God rescues sinners

However, because of God's great love and compassion, he has acted throughout history to save some people. He chose Abraham and through his descendants the nation of Israel. Through the nation of Israel God sent his Son, Jesus Christ 2,000 years ago. (Ephesians 1 v4, 2 v4, Romans 3 v21, Genesis 12 v1, Isaiah 9 & 11)

Jesus

The bible says that Jesus is the Son of God (Mark 1 v1) and that he came to this earth in human flesh, he lived a sinless life and through his blood which he shed on the cross he satisfied the wrath of God against sinners (1 Peter 3 v18, Hebrews 7 v27). People who trust in Jesus can therefore be completely forgiven of their sin (1 John 1 v7), not through what they have done but because Jesus took the wrath of God which they deserved. After Jesus died he was resurrected and after appearing to the disciples (and 500+ others, 1 Corinthians 15 v6) ascended into heaven and is seated at the right hand of God the Father and intercedes for his people i.e. acts as a mediator between man and God (providing Christians access to God, Hebrews 8 v1. Acts 1 v11)

Salvation

Salvation is the work of God who works in his people through his Spirit to bring them to repentance and faith (John 16 v8). Christians therefore have God's Holy Spirit in them who changes them to desire to live a life in accordance to God's will and glory as revealed in Scripture. (Romans 8 v9) When Christians die they will be with God in heaven for all eternity. Jesus will come back and the world will end, there will then be a final judgement where those who have not accepted Jesus will be cast into hell with Satan and his angles. Christians will receive new bodies and live in eternal bliss in the presence of God the Father, God the Son, and God the Spirit. (Hebrews 9 v27, Revelation 20 v11, 1 Corinthians 15 v51)

The biblical way of salvation has often been attacked over the centuries, however it is stated clearly in the 39 Articles of the Church of England:

Article 6: Of the sufficiency of the holy Scriptures for salvation.

Article 1: Faith in the Holy Trinity

Article 9: Of Original or Birth-sin

Article 2: The Word, or Son of God, who became truly man

Article 4: The resurrection of Christ

Article 11: Of the Justification of Man

See also:

Publications relevant to this issue

The Order of Salvation (ordo salutis)

Predestination (God's sovereignty in salvation)

Articles relevant to this issue:

The Atonement in St. Mark's Gospel. Churchman article from 1944 by
J. P. Hickinbotham.

Christ our Righteousness - What did Christ accomplish on the Cross? Cross†Way article by David Streater.

From Darkness to Light - God's Work in Salvation. Cross†Way article by John Cheeseman (Issue 58, 1995)

The English Reformers' Teaching on Salvation. Churchman article by Donald Allister.

ELECTION - God's choice of whom he will save. Cross†Way article by Gerald Burrows.

Toplady on Predestination. Churchman article by Cecil Proctor.

What is Conversion? Churchman article by Tony Baker.

The Centrality of the Cross. Cross†Way article - David Samuel looks at the nature of the Great Commission.

The Third of the Good Friday Collects - A Devotional Study.
Cross†Way article by Gary Townsend.

Satisfaction - Cross†Way Article from 1998 by David Phillips -

The Great Controversy: Which is the Channel of Salvation? Faith? or The Sacraments? Church Association Tract 163.

The Priesthood of Christ. Church Association Tract by J.C. Ryle.

The Relation of Soundness in the Faith to Spirituality in the Life.
C19th Church Association Tract, no. 17 by J. Richardson.

Thy Will Be Done - A Scriptural meditation on Christ's Obedience. Cross†Way article by David Streater.

Hell - A Prime Motive for Evangelism. Cross†Way article by John Cheeseman.

Confession and Forgiveness of Sins. Church Association Tract from C19th explaining from Scripture and Cof E teaching what true confession and forgiveness of sin is and how this differs from Auricular Confession (i.e. confession to a priest).

Gospel Freedom & Priestly Tyranny. C19th Church Association Tract outlining from the bible and official CofE teaching the nature of Christ's sacrificial death and how this contrasts to the errors of ritualism.

Grace Abounding' - Imputed Righteousness in the Life and Work of John Bunyan. Churchman article by Robert Oliver

Free Will and Perseverence - Churchman Article from 1971 by David Broughton Knox

Symposium on Penal Substitution - Cross†Way article.

A report by Mike Ovey on the debate held by the Evangelical Alliance in July 2005 in response to false teaching by Steve Chalke and Alan Mann in a book titled 'The lost message of Jesus' which denied penal substitution.

Children and Their Relationship to Jesus - Cross†Way article by Joy Shearer discussing conversion in children.

Justification: The Reformers and Recent New Testament Scholarship.

Churchman article by Gerald Bray, examining some contemporary theories (or New Perspectives) of Paul's teaching on Justification.

Does the Christian View of Death Need Reviving? Churchman article by Melvin Tinker.

Evangelism - Neglected Perspective. Cross†Way article by Wallace Benn.

Prayers for the Dead. Extract from Homily XIX. Church Association Tract 126.

Prayers for the Dead. Church Association Tract 3.

What's wrong with praying for the dead? Cross†Way article by David Phillips, Autumn 2007. 

What should we pray? - Prayer for the dead in Anglican Liturgy. Cross†Way article by David Phillips, Autumn 2007. 

"To Die is Gain." David Phillips discusses what happens to the believer when they die. Cross†Way article Autumn 2007.

The Invocation of the Saints. Church Association Tract 422.