The Chaplet of Mercy is recited using ordinary rosary beads of five decades. The Chaplet is preceded by two opening prayers from the Diary of Saint Faustina and followed by a closing prayer.
 
1. Make the Sign of the Cross

In the name of the Father, and of the Son, and of the Holy Spirit. Amen.

2. Optional Opening 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.

(Repeat three times)

O Blood and Water, which gushed forth from the Heart of Jesus as a fount of mercy for us, I trust in You!

3. Our Father (On the first bead of the three)

4. Hail Mary (On the second bead of the three) 

5. The Apostles’ Creed (On the third bead of the three)
 
6. The Eternal Father (On the Our Father Beads)

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.

7. On the 10 Small Beads of Each Decade

For the sake of His sorrowful Passion, have mercy on us and on the whole world.

8. Repeat for the remaining decades

Saying the "Eternal Father" (6) on the "Our Father" bead and then 10 "For the sake of His sorrowful Passion" (7) on the following "Hail Mary" beads.

9. Conclude with Holy God (Repeat three times)

Holy God, Holy Mighty One, Holy Immortal One, have mercy on us and on the whole world.

10. Optional Closing Prayer

Eternal God, 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.

Pray the Novena

A novena is typically nine days of prayer in preparation of a celebration of a feast day. At the National Shrine of The Divine Mercy, the Chaplet of Divine Mercy Novena is recited perpetually at the Hour of Great Mercy — the three o'clock hour.

Read more here about the Hour of Great Mercy here

The Chaplet can be said anytime, but the Lord specifically asked that it be recited as a novena. He promised, "By this Novena (of Chaplets), I will grant every possible grace to souls."
 

Divine Mercy Novena Prayer - Pray this after completing the Chaplet
 

The following is the same prayer being said during the Novena at the National Shrine of The Divine Mercy. Novena to The Divine Mercy:
 

 "I desire that during these nine days you bring souls to the fountain of My mercy, that they may draw therefrom strength and refreshment and whatever grace they need in the hardships of life, and especially at the hour of death." (Diary, 1209)