When did communion start in the church?

Answer 1

It would seem that, historically, Catholic deacons would have always been ministers of Holy Communion.

For some centuries, as attested by Justin Martyr, Cyprian of Carthage and others, deacons were the only ministers of communion - even presbyters (priests) had to receive communion from the deacons and were chastised "if, through their presumption, they take the chalice from the table of the Lord unless it is handed to them by the deacon" (Isidore of Seville).

We have evidence of the third century martyr, St. Tarcisius, bringing Communion to prisoners condemned to death when he was assaulted and murdered. He gave up his life rather than surrender the Eucharist to the mob who killed him. He was an acolyte... a minister in 'minor orders' and not even a deacon. Presumably a deacon would be a proper minister of the Eucharist if an acolyte was serving as a minister of Holy Communion. By the 4th century, there was a question presented to the First Council of Nicea which asked if deacons should be allowed to give communion to priests... this practice was forbidden. Again, this implies that deacons were historically engaged in giving Holy Communion.

In the West, the Tridentine practice was to limit deacons as "extraordinary" ministers of the Eucharist... that is, they would minister the Eucharist when the parish priest was unavailable, and then, only at his deputation. A deacon could also preside at and give Eucharistic benediction.

In fact, the re-introduction of deacons as a 'full and permanent order' in the Catholic Church was, among other reasons, an effort to provide proper ministers of communion in remote villages where a priest could not come on a regular basis. The (rather novel) institution of lay extraordinary ministers of the Holy Communion since the council seems to have made this initial reasoning for the permanent diaconate moot. Nonetheless, there is now a fully-restored permanent diaconate in the Western Church, thankfully, to serve in the many valuable ministries of that order.

Current practice of the Church is to recognize deacons, by virtue of their ordination, as 'ordinary' ministers of the Eucharist alongside priests and bishops. They should always accept and undertake this ministry ahead of other lay ministers of Holy Communion at all times unless impeded for a good reason. Deacons normally (but not exclusively) offer the chalice to the faithful when both species are offered.

Answer 2

Communion started just before Jesus' death in the Upper Room before they went to the Garden of Gethsemane. It is done in our churches and elsewhere to remember what Jesus did for us until He comes again.