The Holy Spirit is the spirit of the Father. So said the disciples/Apostles who should know what they write about.
for the Holy Spirit will teach you in that very hour what you ought to say." Luke 12:12
for it will not be you speaking, but the Spirit of your Father speaking through you. Matthew 10:20
These man were taught by Jesus all that they understood. Jesus promised that they would be guided by the spirit on his departure. Here they are worshipping and praying - we know that this is a matter of the spirit in them guiding, and granting them awareness of what they should be focussing on.
And behold, I am sending the promise of my Father upon you. But you, remain in the city until that you should be clothed with power from on high. Luke 24:49
What is that 'power'? They don't have super-human strength or strange magical abilities - they have the presence of God within them (just as Jesus did), which opposes the natural human spirit of self and enables the works of God which are not part of the natural man.
They hear the word of God in their spirit as God joins His spirit with them - knowing the things of God, the truth of His word, the correct way to deal with matters at hand, the words to use at each opportunity.
The spirit testifies with our spirit that we are children of God Rom 8:16
the Holy Spirit will teach you in that very hour what you ought to say.
The spirit is the Father - sometimes there is record of an audible message, mostly there is not, but we understand by drawing near to God (as they were doing) what our path and words should be - as they did.
The whole reason for fasting and prayer is to seek God's will in an important matter. They subsequently, and apparently, collectively, understood how God wanted them to proceed by the word He placed in their minds.