Faith, scripture, grace
1) Sola fide ("by faith alone").
"The just shall live by faith." (Romans 1:17)
Humans can gain salvation through faith, rather than through "good works" or the dispensations of the Church. Until the Reformation, the Church held an effective monopoly on God's grace, which was dispensed through the sacraments* and guaranteed by the granting of indulgences*. The doctrine of justification by faith alone removed the need for a priestly hierarchy to mediate between God and the individual.
2) Sola scriptura ("by Scripture alone")
Religious truths can be known only through reading the Word of God as revealed in the Bible. This principle opened the door for "radical" interpretations of God's Word, bringing those Catholic doctrines and rituals under attack which had uncertain Scriptural grounds*.
3) Sola gratia ("by grace alone")
"For by grace are ye saved, through faith, and that not of yourselves: it is the gift of God: Not of works, lest any man should boast." (Ephesians 2:8-9).
Humans are innately evil, incapable of either knowing religious truth or acting for the good without God's grace. Faith is only in the gift of God, and only through His inscrutable mercy are an elect few granted salvation. The Reformed Churches thus adopted a belief in predestination and the enslavement of the will by the flesh for those not predestined to salvation.
Footnotes
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The sacraments
The seven sacraments recognized by the Roman Catholic Church are: baptism, confirmation, the Eucharist, penance, extreme unction (anointing of the sick), matrimony, and ordination.
The Eucharist is a reenactment of Christ's Last Supper with his disciples; partaking in "communion" is believed to unite the believer with Christ and fellow Christians. Conflict over the doctrine of transubstantiation, according to which the bread and wine of communion become the substance of Christ, was one of the main points of controversy resulting from Luther's doctrine.
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Indulgences
According to papal theory in the Middle Ages, Christ's sacrifice was more than enough to redeem the human race, leaving a treasury of forgiveness that could be dispensed by the popes. Indulgences granted full or partial relief from the punishment for sins in purgatory, provided the recipients had repented before death. Their use, reserved at first to the pope, degenerated by the 15th century into the sale of indulgences by clergymen with papal commissions, which were often forged.
In the Canterbury Tales Chaucer satirizes a Pardoner who sells fake religious relics.
His wallet lay before him on his lap,
Brimful of pardons come from Rome, all hot. . . .
. . .in his trunk he had a pillow-case
Which he asserted was Our Lady's veil. . . .
He had a cross of metal set with stones
And, in a glass, a rubble of pig's bones.
And with these relics, any time he found
Some poor up-country parson to astound,
In one short day, in money down, he drew
More than the parson in a month or two.
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Protestant sacraments
Luther rejected all of the sacraments except baptism and the Eucharist, which was modified as the "Lord's Supper."
The Lutherans followed the doctrine of consubstantiation, by which the bread and wine of communion "join" with Christ's body and blood, as opposed to transforming into it. Zwinglians and Calvinists rejected the Real Presence entirely, one group holding that communion was only symbolic and the other that Christ's spirit alone was present.