Prokeimenon
A prokeimenon (or prokimen; plural: prokeimena) is a liturgical verse or scriptural passage sung or read before the apostolic reading. It can serve as an introduction to the theme of the particular reading on feast days. On most Sundays, the prokeimenon of the resurrection, for the tone of the week (from the Octoechos), is chanted.
At the Divine Liturgy
At the Divine Liturgy, the prokeimenon is proclaimed after the singing of the Trisagion hymn to introduce the apostolos reading. The deacon says, "Let us attend." At this point the Greek and Slavic practices diverge.
Greek practice:
Deacon: Let us attend.
Reader (facing altar): [chants the first and second lines of the prokeimenon in the appropriate mode/tone]
Deacon: Wisdom.
Reader (facing altar): [announces the source of the epistle, e.g., "the reading is from the Epistle of St. Paul to the Ephesians"]
Deacon: Let us attend.
Reader (turning to face people): [chants epistle in the free-form Byzantine style]
Priest: Peace be to thee that readest.
Slavic practice:
Priest: Peace be unto all.
Reader (facing altar): And to thy spirit.
Deacon: Wisdom.
Reader: [announces the prokeimenon and its tone, then intones first verse of the prokeimenon text]
Choir: [repeats first verse melodically]
Reader: [intones second verse]
Choir: [repeats first verse melodically]
Reader: [repeats first half of first verse]
Choir: [finishes with second half of first verse]
Deacon: Wisdom.
Reader: [announces source of the epistle]
Deacon: Let us attend.
Reader: [intones epistle in monotone or with the Russian "step method"]
Priest: Peace be to thee that readest.
Alleluia verses
The Prokeimenon sung immediately before the Gospel Lesson is called the Alleluia.
At other services
Other services may have the chanters (Greek) or priest or deacon (Slavic) proclaim the prokeimenon before an Old Testament reading.