What Should We Do After Holy Communion?

After Holy Communion we should spend some time adoring Our Lord, thanking Him, renewing our promises of love and of obedience to Him, and asking Him for blessing for ourselves and others.

We should not leave the church immediately after receiving Holy Communion. We should pray at least ten or fifteen minutes, thanking our Divine Guest. We should thank Our Lord fervently for coming to us, make acts of faith, adoration, humility, and love, and beg Him for ourselves and those we love. 

Our Lord is actually and personally present in us as long as the appearance of bread remains, for at least ten minutes after receiving Holy Communion. Shall we treat God the Son coldly, by doing nothing when He comes? For earthly guests we exert ourselves to utmost, to entertain them and make their stay enjoyable. Shall we then say to Christ, "I am glad You came, Lord. Now goodbye, because I must go home." And forget Him?

2. If our work or duties prevent our staying in church to give proper thanksgiving, let us remain recollected and in union with Jesus on our way home; and let us remember Him with love throughout the entire day. 

Once St. Philp Neri noticed that a certain parishioner, for no reason, habitually left the church immediately after receiving Holy Communion. In order to correct him, he told two acolytes one day to accompany the man with lighted candles as he walked home. The acolytes did as they were told. The people in the streets, and the man seeing his escort asked them the reason for their following him. They replied that Father Philip Neri had so instructed them. The man returned to the church to find out St. Philip's purpose. The Saint answered, "We have to pay proper respect to Our Lord, Whom you are carrying away with you. Since you neglect to adore Him. I sent two acolytes to take your place." Realizing his fault, the man knelt and made the proper thanksgiving after Holy Communion. 

Source:  My Catholic Faith

NOTE: Do not forget that you must receive Communion in a state of sanctifying grace, that is, without having committed any mortal sin since your last good Confession (with true contrition and purpose of amendment).

Likewise, never allow the consecrated Host to be given to you in the hand, as your hand is not consecrated and, furthermore, consecrated particles—where Christ is fully present—can frequently remain on them and subsequently fall to the ground where they could be trampled. Every member of the faithful has the right to receive Christ in the consecrated Host on the tongue and kneeling, which is the best way to show reverence to the Eucharist