The previous posts in this series were:
1a. Born at a Time and Place 1; 1b. Born at a Time and Place 2
2a. A Change in Life Direction; 2b A Change in Life Direction 2; 2c A Change in Life Direction 3
3a. The Unknown Years 1; 3b. The Unknown Years 2; 3c. The Unknown Years 3
Acts 18 is very specific about the Roman governor at Corinth at the end of Paul's almost two years there. It was a man named Gallio. By happy archaeological fortune, we can date Gallio's governorship in Corinth to around AD51-52. All in all, it fits very well with Acts to think that Paul was in Corinth from around AD50-52.
We left Paul in the last chapter around the year AD49. Around that year Paul was in Jerusalem over the issue of whether Gentiles needed to convert fully to Judaism to be saved.  So the chronology of Acts here works very well with what we know from elsewhere. Paul has an argument with Barnabas over going on a second missionary journey together in AD49. Barnabas and his cousin John Mark head off for Cyprus again. Paul picks up another man named Silas and heads off toward his home region of Cilicia, where Tarsus was.
So Paul and Barnabas effectively split up the territory of the earlier journey they took together. Paul and Silas go back to the northern half. They visit cities like Derbe, Lystra, Iconium, and another city in the region with the same name of Antioch like the place they launched from. Perhaps most scholars think that this is the region to which Paul would write the book of Galatians a little bit later. Many other conservative scholars think Paul had already written Galatians to this region by now. We will later fly a less popular suggestion, although the one that was the majority position throughout church history, namely, that Paul wrote Galatians to the area just north of these cities.
At Lystra, Acts 16 tells us Paul and Silas pick up a young man named Timothy. Acts also surprisingly tells us that Paul has him circumcised. We have no basis to doubt Acts about this claim, although it is curious. Paul in Galatians will argue that these Gentiles will fall from grace if they become circumcised (Gal. 5:2-4). So why would he circumcise Timothy?
If as we think Galatians came later, Paul might still have been working through his "policies" on these things at the time. Nevertheless, Acts implies Paul did so because Timothy's mother was Jewish (cf. Acts 16:1). In the case of Titus, the argument goes, Titus was fully Gentile, so Paul did not have him circumcised (cf. Gal. 2:3). This seems a very plausible explanation to us. Perhaps Paul is thinking that a circumcised Timothy might help him liaise with Jews, while an uncircumcised Timothy would simply be unused potential.
Whatever practical advantages circumcising Timothy brought Paul, his opponents apparently would later use it against him. Assuming that Paul wrote Galatians later than this point in time, some of Paul's opponents may very well have used the fact that Paul circumcised Timothy to claim that even Paul had been won over to the idea that circumcision was preferable (cf. Gal. 5:11). And so Paul reassured them that he was not still preaching circumcision.
Acts 16 tells us that Paul then went through the region of Galatia and Phrygia with Silas (Acts 16:6). Interestingly, Acts apparently does not include the region of Iconium, Lystra, and Derbe in "Galatia" here, which presents a minor objection to the idea that these are the churches to which Galatians is written. We would go with what most interpreters thought throughout church history, namely, that it was at this point that Paul founded some churches in the north. This was the region that had properly been known as Galatia before the Romans consolidated north and south. So in our theory, Paul founds some churches in north Galatia, which becomes the primary audience of the letter to the Galatians. These would be churches in the vicinity of Ancyra in modern day Turkey, churches about which Acts does not give us any details.
Paul would eventually follow the Roman roads north to Troas and then would sense God calling him to jump the Bosphorus into Macedonia. The rest is history. Paul founds the church at Philippi, apparently one of his favorite churches. He will found the church at Thessalonica. Acts tells us he and Silas found a church in Berea, heading south into Greece proper. He will stop shortly in Athens, but then will move on to Corinth. At Corinth he will find his groove and stay for almost two years.
Paul's writings themselves tell us little of his time in Philippi and Thessalonica, and nothing of his time in Berea. Acts tells us he was jailed for a night in Philippi, that an earthquake hits the jail, and that he is freed to go the next day. The letter of 1 Clement, probably written at the end of the first century, mentions seven imprisonments of Paul. If this number is not symbolic, perhaps Philippi was the first or second time, although it is of course possible Paul encountered the Roman governor of Cyprus after a similar night in the brig (cf. Acts 13:7).
Paul does not stay long at all at Thessalonica. Acts gives us the impression it might have been as little as three Saturdays, but it was probably at least a little longer. Philippians 4 indicates that the church at Philippi sent him material support more than once while he was there. Also, while Acts as it usually does focuses on the Jews and their opposition to Paul, 1 Thessalonians is overwhelmingy directed at Gentiles, implying that Paul's most fruitful ministry in the city was not in the synagogue. Perhaps Paul was there a couple months, just long enough to get the plane headed down the runway, although he is forced to leave before he can see the plane take off (cf. 1 Thess. 1:17).
For whatever reason, Paul does not stay long in Athens. According to 1 Thessalonians 3:1-2, Paul and Silas send Timothy back to Thessalonica from there.  They are worried about whether the church has successfully launched. Paul does not write 1 Thessalonians until Timothy has returned with news of the church. We cannot tell whether Paul has already moved on to Corinth by that point, but it seems reasonable, assuming Paul did not stay long in Athens.
Acts 17 gives us a brilliant speech by Paul to the Areopagus, the ruling council of the city. It is thus possible that Paul spent yet another night or two in jail there before seeing the council, perhaps making the second or third of his supposed imprisonments. The impression we get is that Paul's charge has to do with promoting a unfamiliar cult, something that concerned the Romans then as Homeland Security might today. As in Thessalonica, the city seemed to be content with telling Paul to move on...
 Whether you think this event was more like a private visit as in Galatians 2, a public Jerusalem Council as in Acts 15, or something in between the two.
 The scenario of 1 Thessalonians is in minor tension with the account in Acts. In Acts 17:15, Paul goes on to Athens from Berea alone and both Silas and Timothy stay in Berea. Then Paul continues on to Corinth still alone from Athens (18:5). But in 1 Thessalonians, Paul, Silas, and Timothy have all gone to Athens, and it is from there that Timothy alone returns to Thessalonica.