Here are the prayers the priest says before and after Communion. They are suitable for lay people as well, or you might them to be inspirational models for your own prayer:
From The Prayer of St. Ambrose (pre-Mass preparatory prayer)
Grant this this sacred foretaste of your Body and Blood
which I, though unworthy, intend to receive,
may be the remission of my sins, the perfect cleansing of my faults,
the banishment of shameful thoughts, and the rebirth of right sentiments;
and may it encourage a wholesome and effective performance
of deeds pleasing to you,
and be a most firm defense of body and soul
against the snares of my enemies.
Lord Jesus Christ, Son of the living God (pre-Communion prayer)
Lord Jesus Christ, Son of the living God,
who, by the will of the Father
and the work of the Holy Spirit,
through your Death gave life to the world,
free me by this, your most holy Body and Blood,
from all my sins and from every evil;
keep me always faithful to your commandments,
and never let me be parted from you.
May the receiving of your Body and Blood (pre-Communion prayer)
May the receiving of your Body and Blood, Lord Jesus Christ,
[which I, though unworthy, presume to receive (*1962 Missal includes this phrase)]
not bring me to judgment and condemnation,
but through your loving mercy
be for me protection in mind and body
and a healing remedy.
May the Body/Blood of Christ (Communion prayer)
May the Body of Christ keep me safe for eternal life.
May the Blood of Christ keep me safe for eternal life.
Bread of Heaven (Communion prayer in the 1962 Missal)
I will take the Bread of Heaven, and will call upon the name of the Lord.
Chalice of Salvation (Communion prayer in the 1962 Missal)
What return shall I make to the Lord
for all the things that He has given to me?
I will take the chalice of salvation,
and call upon the Name of the Lord.
I will call upon the Lord and give praise:
and I shall be saved from my enemies.
What has passed our lips... (post-Communion prayer)
What has passed our lips as food, O Lord,
may we possess in purity of heart,
that what has been given to us in time
may be our healing for eternity.
May your Body, O Lord (1962 Missal post-Communion prayer)
May Your Body, O Lord, which I have received
and Your Blood which I have drunk,
cleave to my inmost parts,
and grant that no stain of sin remain in me,
whom these pure and holy Sacraments have refreshed.