History

Between 1931 and 1938, Our Lord appeared to St. Maria Faustina, and reminded the world, through her, about His love for all humanity.1
In 1935, through a vision and interior voice, she was given a powerful prayer that drew upon the mercy of God. This prayer eventually became the Chaplet of the Divine Mercy.2
The Promise
As per St. Faustina, Our Lord said the following:
Encourage souls to say the Chaplet which I have given you (1541). Whoever will recite it will receive great mercy at the hour of death (687). – Diary of St. Faustina2
Structure & Schedule
The Chaplet of Divine Mercy is recited on Rosary beads. The Chaplet can be said on any day at any time. However, it is favorable to recite it at 3 pm, the hour when Our Lord died on the Cross.2

Order of Prayers

Begin the Chaplet by saying the following prayers:
You expired, Jesus, but the source of life gushed forth for souls, and the ocean of mercy opened up for the whole world. O Fount of Life, unfathomable Divine Mercy, envelop the whole world and empty Yourself out upon us.
O Blood and Water, which gushed forth from the Heart of Jesus as a fount of mercy for us, I trust in You! (recite 3 times)

Repeat the following sequence 5 times:
Eternal Father, I offer you the Body and Blood, Soul and Divinity of Your Dearly Beloved Son, Our Lord, Jesus Christ, in atonement for our sins and those of the whole world.
For the sake of His sorrowful Passion, have mercy on us and on the whole world (recite 10 times)

Conclude the Chaplet by saying the following prayers:
Holy God, Holy Mighty One, Holy Immortal One, have mercy on us and on the whole world (recite 3 times)
Let us pray:
Eternal Father, in whom mercy is endless and the treasury of compassion — inexhaustible, look kindly upon us and increase Your mercy in us, that in difficult moments we might not despair nor become despondent, but with great confidence submit ourselves to Your holy will, which is Love and Mercy itself.
+ Amen +
Prayer referenced from The Divine Mercy