Let’s start with the question: why does he have three so-called “missionary journeys” when it seems he was engaged in mission work (Acts 9:19b-20, 23, 26-27; 11:25-26) before the dating of the “first” journey?
The three journeys of Paul do not indicate when he first commenced mission work. The three journeys, instead, have a common launching point: Antioch of Syria.
Paul’s first journey from Syrian Antioch is highlighted in Acts 13–14 (13:1-3; 14:26-28). He launches from, and then returns to, that city.
Paul’s second journey from Syrian Antioch is highlighted in Acts 15:36–18:22 (15:36-41; 18:22). Paul launched from, and returned to, that city.
Paul’s third journey from Syrian Antioch is highlighted in Acts 18:23–21:16 (18:23; 21:16). Although Paul launched from Syrian Antioch this third time, he didn’t return there. Instead, his journey ended with his arrival in Jerusalem (21:17), soon after which he was arrested (21:27-36).
When scholars talk about Paul’s three missionary journeys, then, they are referring to the three mission ventures that were each launched from Syrian Antioch.
Now let’s talk dates (which, of course, are probable estimates):
(1) AD 46-48, Paul’s first journey from Syrian Antioch (Acts 13–14)
(2) AD 50-52, Paul’s second journey from Syrian Antioch (Acts 15:36–18:22)
(3) AD 53-57, Paul’s third journey from Syrian Antioch (Acts 18:23–21:16)
At the beginning of the second (16:1-6) and third journeys (18:23), Paul revisited churches in southern Galatia that he established during the first journey (13:4–14:26).
In his second missionary journey, Paul mainly focused on Corinth (18:1-18), remaining there for a little less than 2 years.
In his third missionary journey, Paul mainly focused on Ephesus (19:1-41), remaining there for almost three years (20:31).
Understanding these aspects of Paul’s three missionary journeys is important, since their narratives comprise almost all of Acts 13–21 (the exception being the event and outcome of the Jerusalem Council in Acts 15:1-35). Therefore, neglecting study of Paul’s missionary journeys will handicap one’s grasp of a large chunk of the Book of Acts.