Ordinary ministers of the Eucharist are instructed to make this ministry an ordinary part of their duties:
17. It is, first of all, the office of the priest and the deacon to minister holy communion to the faithful who ask to receive it. (Eucharisticum mysterium 31) It is most fitting, therefore, that they give a suitable part of their time to this ministry of their order, depending on the needs of the faithful.
A lay person instituted as an acolyte may also serve. Note the conditions when this is advisable:
It is the office of an acolyte who has been properly instituted to give communion as a special minister when the priest and deacon are absent or impeded by sickness, old age or pastoral ministry or when the number of the faithful at the holy table is so great that the Mass or other service may be unreasonably protracted. (Paul VI, apostolic letter Ministeria quaedam, August 15, 1972, no. VI)
Failing those conditions, a lay person may serve if the local bishop permits it.
The local Ordinary may give other special ministers the faculty to give communion whenever it seems necessary for the pastoral benefit of the faithful and a priest, deacon, or acolyte is not available. (CDWDS instruction Immensae caritatis, January 29, 1973, 1, I and II.)
Where may a Communion service take place? There is a hierarchy of preferred places:
18. The place where communion outside Mass is ordinarily given is a church or oratory in which the eucharist is regularly celebrated or reserved or a church, oratory, or other place where the local community regularly gathers for the liturgical assembly on Sundays or other days. Communion may be given, however, in other places, including private homes; when it is a question of the sick, prisoners, or others who cannot leave the place without danger or serious difficulty.
Did you notice the distinction between offering a Communion service in a church, oratory, or other place, and the limitation being lifted for where the sacrament itself may be given? Any comments on this?