Most of the believers, other than the Apostles, leave Jerusalem from fear of Saul and other authorities, nut this just spreads the gospel to travelling Ethiopian eunuchs and to people in cities, including Samaria, Damascus (where Saul is converted), and Lydda and Joppa (where Dorkas is raised from the dead): Acts 8–9
After Stephen was stoned, Saul (later renamed to Paul) started his house-to-house search for other followers of Jesus. It lead to almost all of them fleeing Jerusalem:
Acts 8:1-3 A great wave of persecution began that day, sweeping over the church in Jerusalem; and all the believers except the apostles were scattered through the regions of Judea and Samaria. (Some devout men came and buried Stephen with great mourning.) But Saul was going everywhere to destroy the church. He went from house to house, dragging out both men and women to throw them into prison.
It would have been a terrifying time for Jerusalem’s new believers. Sadly, it wouldn’t be the last time ever that someone would persecute believes in this way.
How did the apostles manage to avoid capture? Perhaps there was a limit; let the leaders stay free (because they were too popular), but kill off the followers. Perhaps the apostles were just too good at hiding themselves, moving from house to house and managing, somehow, to stay one step ahead of Saul. There’s no evidence either way.
Many years later, Saul said he was authorised by the High Council to do this:
Acts 26:9-10 I used to believe that I ought to do everything I could to oppose the very name of Jesus the Nazarene. Indeed, I did just that in Jerusalem. Authorized by the leading priests, I caused many believers there to be sent to prison.
Even so, there is no record that he had any material help from them. It was Saul who went house to house, and it was Saul who headed to Damascus for a conversion he wasn’t expecting:
Acts 9:1-2 Meanwhile, Saul was uttering threats with every breath and was eager to kill the Lord’s followers. So he went to the high priest. He requested letters addressed to the synagogues in Damascus, asking for their cooperation in the arrest of any followers of the Way he found there. He wanted to bring them—both men and women—back to Jerusalem in chains.