Adam Clarke on Acts 13:2

As they ministered to the Lord, and fasted - On Mondays and Thursdays it was usual with the more pious Jews to attend the public service in their synagogues, and to fast: the former is what we are to understand by ministering to the Lord. On the Sabbaths they attended the service in the synagogue, but did not fast. The Greek word, λειτουργουντων, signifies performing the office of praying, supplicating, rendering thanks, etc.: hence the word λειτουργια, liturgy, the work of prayer, etc., from λιτη, supplication, according to some; or rather from λειτος, common, and εργον, work, the common or public work, in which all the people were engaged.

The Holy Ghost said - A revelation of the Divine will was made to some person then present; probably to either Simeon, or Lucius, or Manaen, mentioned before.

Separate me Barnabas and Saul - Consecrate, or set them apart, for the particular work whereunto I have called them. How this was done, we find in the next verse.