As we have been told by Saint John Vianney, you should not immediately pray some formally made prayer, such as ones made specifically for thanksgiving after communion,
but instead you should pray to God from your own heart and mind, because to pass those precious moments filled with the words of others is not quite as profitable as just speaking to God from your own love and affections, even to spend those moments just listening to God is more profitable,
the church has taught that after receiving, we should silently and humbly walk back to our seat with our head bowed, and speak to our Divine Saviour in a way which we humble ourselves before Him, thank Him, offer ourselves up to Him, express our love, and implore His grace.
you can thank God for all the things you feel grateful for, and also the things you should be grateful for, especially the communion you are then having,
we are so thankful for the least gifts received by friends and relatives, how much more thankful should we be, then, for the greatest gift we could ever receive, by and of God Himself?
you can offer yourself up to God by promising to be His entirely, and to remain forever, you can pray something such as “I am Thine, dear Jesus, in life and death”.
To express your love to God, although words from your heart are good, but they are empty without action, so we should strive not just to show our love to God during our communion with Him, but always in everything we do, such as avoiding evil, and patiently enduring sufferings and afflictions, being kind and charitable to others, practice all of our virtues and pray often and always, and everything else we are told to do by God and His church.
and in order to do that, we must implore His grace, especially by imploring God that we may ever remain united with Jesus and never be separated from Him by sin.
there are 4 graces in particular that Holy Communion imparts to our soul,
first, It unites us most intimately with Christ and increases sanctifying grace in us, second, It weakens our evil inclinations and gives us a desire and strength to combat them, and to do good, third, It cleanses us from venial sin and preserves us from mortal sin, and four, it is to us a pledge of our future resurrection and everlasting happiness.
after communion, which as we are told lasts about 15 minutes, then it is good to read from your prayer book whatever you want,
of course there are no “rules” in what you must pray during communion, so it is for you to decide, but i hope that this helps you in deciding anyways.
you should also stay afterwords for some time, if it is possible, just to stay in grateful and loving silence with God,
it is also always a good idea to go to confession before communion, even with just venial sins, because although we can receive with venial sins on our soul, they still take away from our communion with God, because venial sins lessen the graces you would otherwise receive, since they draw our souls to created things, and away from that which our souls were created for - which is God.
there should be a period of preparation before communion - by pious meditations, devout exercises, prayer, zeal, and devotion, and then there should be a period of thanksgiving afterwords, which may go on in several ways for as long as you want.
and of course, these things are not obligatory, but they are still very beneficial to you, and very pleasing to God, and by such practices you deepen and grow in your relationship with God.
and above all, if you wish to please God and know, love, and serve Him well, just ask Him to help and guide you, and He will, pray to Him often, go to Him with all your questions and problems and everything, be like a child to Him, as He tells us, and He will take care of your every need.
well, that’s all for now, but if you would like to be instructed more in all of the practices for Holy Communion, i’d be glad to help.
ok, hope this helps, take care.