The Chaplet of the Divine Mercy is prayed on ordinary Rosary beads:

3 O'Clock Prayer  (optional for other times)

3 O'Clock Prayer
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, O unfathomable Divine Mercy, envelop the whole world and empty Yourself out upon us.

O Blood and Water, which gushed from the Heart of Jesus, as a fountain for us, we trust in You. (3 times 'O Blood and Water)
 

Opening Prayers - on the first 3 beads after the Cross

The Lord's Prayer
Our Father, Who art in heaven, Hallowed be Thy Name.
Thy Kingdom come, Thy Will be done, on earth as it is in Heaven.
Give us this day, our daily bread,
And forgive us our trespasses,
as we forgive those who trespass against us.
And lead us not into temptation, but deliver us from evil.
Amen.

Hail Mary
Hail Mary full of Grace, the Lord is with thee.
Blessed are thou amongst women
and blessed is the fruit of thy womb Jesus.
Holy Mary Mother of God,
pray for us sinners now and at the hour of our death.
Amen

Apostle's Creed
I believe in God, the Father almighty,
Creator of heaven and earth, and in Jesus Christ, his only Son, our Lord.
He was conceived by the power of the Holy Spirit
and born of the Virgin Mary.

He suffered under Pontius Pilate,
was crucified, died, and was buried.
He descended into hell.

On the third day he rose again from the dead.
He ascended into heaven
and is seated at the right hand of God the Father Almighty.
From there He will come to judge the living and the dead.

I believe in the Holy Spirit,
the holy catholic Church,
the communion of saints,
the forgiveness of sins,
the resurrection of the body,
and the life everlasting.
Amen.

On the  1 'Our Father' bead of each decade pray:

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.

On the 10 'Hail Mary' beads of each decade pray:

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

Closing Prayers

(At the end of the 5 decades)

Holy God, Holy Mighty One, Holy Immortal One, have Mercy on us and on the whole world. (Repeat 3 times)

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, so that in difficult moments, we may not despair nor become despondent but with great confidence, submit ourselves to Your Holy Will, which is Love and Mercy itself. Amen.