Proclamations and Conversions Discussed in Both Acts and Epistles: Corinth
The church at Corinth was started during the apostle Paul's second missionary journey after stops in Philippi, Thessalonica, Berea and Athens. Paul wrote 1 Corinthians letter from Ephesus, his next stop on the mission field after Corinth.

There have been many attempts to re-construct the various letters back and forth between Paul and the Corinthians. More detail on this study beyond the scope of our study here and not especially relevant. We do know that the primary occassion of the first (canonical) Corinthian letter was the problem that had developed in the Corinth with attaching far to much importance to the various ministers of the word. The Corinthians had also written some questions on various miscellaneous matters (including clarifications on items from what seems to have been a previous letter from Paul) , which he addressed point by point. It is also evident that he plans a future visit. The second (canonical) Corinthian letter doesn't discuss matters of the Corinthians' conversion at all, though it is quite a glimpse into Paul's own thinking and motives concerning his ministry in general terms.
 

Text Observations
AC 18:1 After these things he left Athens and went to Corinth. [2] And he found a certain Jew named Aquila, a native of Pontus, having recently come from Italy with his wife Priscilla, because Claudius had commanded all the Jews to leave Rome. He came to them, [3] and because he was of the same trade, he stayed with them and they were working; for by trade they were tent-makers. [4] And he was reasoning in the synagogue every Sabbath and trying to persuade Jews and Greeks. Paul arrived at Corinth and went into the synagogue every Sabbath, reasoning (dielegeto) and  trying to persuade (peitho) Jews and Greeks (that is, God-fearers). 

 
AC 18:5 But when Silas and Timothy came down from Macedonia, Paul began devoting himself completely to the word, solemnly testifying to the Jews that Jesus was the Christ. [6] And when they resisted and blasphemed, he shook out his garments and said to them, "Your blood be upon your own heads! I am clean. From now on I shall go to the Gentiles." [7] And he departed from there and went to the house of a certain man named Titius Justus, a worshiper of God, whose house was next to the synagogue.  On other days of the week, he was working with (and living with!) a fellow Jew named Aquila and his wife Priscilla. Once Silas and Timothy return, Paul devotes himself to the ministry exclusively, solemnly testifying (diamarturoo) to the Jews that Jesus was the Christ. There was some negative response which led Paul to leave the synagogue and go next door. 
AC 18:8 And Crispus, the leader of the synagogue, believed in the Lord with all his household, and many of the Corinthians when they heard were believing and being baptized. However, Crispus the synagogue leader and all his household are said to have believed. In addition, many Corinthians heard, believed and were baptized. 

(Again, a household is said to have believed and been baptized)
AC 18:9 And the Lord said to Paul in the night by a vision, "Do not be afraid any longer, but go on speaking and do not be silent; [10] for I am with you, and no man will attack you in order to harm you, for I have many people in this city." [11] And he settled there a year and six months, teaching the word of God among them. Paul is given a vision encouraging his perseverance in Corinth. Again, we see the idea that God is actively behind this particular ministry in this particular place at this particular time.  Thus, Paul stayed and taught the word for a year and a half. 
AC 18:27 When Apollos wanted to go to Achaia, the brothers encouraged him and wrote to the disciples there to welcome him. On arriving, he was a great help to those who by grace had believed. [28] For he vigorously refuted the Jews in public debate, proving from the Scriptures that Jesus was the Christ. After the departure of Paul and his companions, Apollos (now accurately instructed in the way) takes up the debate with the Jews that Jesus is the Christ. 
1 CO 1:14 I thank God that I baptized none of you except Crispus and Gaius, [15] that no man should say you were baptized in my name. [16] Now I did baptize also the household of Stephanas; beyond that, I do not know whether I baptized any other. [17] For Christ did not send me to baptize, but to preach the gospel, not in cleverness of speech, that the cross of Christ should not be made void. Here we find that Paul personally baptized a small number of people when the church first began. 

(Interestingly, Acts 18:8 says Crispus "believed", but here we find that he was baptized by Paul personally. This illustrates that Luke often refers to one element of conversion rather than mentioning all elements each time. )

Some have attempted to minimize the importance of baptism on the basis of v. 17 but the point of this passage is that many could physically perform baptisms but that Paul was uniquely commissioned to preach the gospel. And-- Paul still personally baptized some. 
1CO 1:18 For the word of the cross is to those who are perishing foolishness, but to us who are being saved it is the power of God. [19] For it is written,
  "I will destroy the wisdom of the wise,
  AND THE CLEVERNESS OF THE CLEVER I WILL SET ASIDE."

  1CO 1:20 Where is the wise man? Where is the scribe? Where is the debater of this age? Has not God made foolish the wisdom of the world? [21] For since in the wisdom of God the world through its wisdom did not come to know God, God was well-pleased through the foolishness of the message preached to save those who believe. [22] For indeed Jews ask for signs, and Greeks search for wisdom; [23] but we preach Christ crucified, to Jews a stumbling block, and to Gentiles foolishness, [24] but to those who are the called, both Jews and Greeks, Christ the power of God and the wisdom of God. [25] Because the foolishness of God is wiser than men, and the weakness of God is stronger than men.

 This passage shows that the proclamation of the cross was central to his message. Indeed, Jews looked for signs and Greeks looked for wisdom, but to them the cross was respectively a stumbling block and foolishness.
1CO 1:26 For consider your calling, brethren, that there were not many wise according to the flesh, not many mighty, not many noble; [27] but God has chosen the foolish things of the world to shame the wise, and God has chosen the weak things of the world to shame the things which are strong, [28] and the base things of the world and the despised, God has chosen, the things that are not, that He might nullify the things that are, [29] that no man should boast before God. [30] But by His doing you are in Christ Jesus, who became to us wisdom from God, and righteousness and sanctification, and redemption, [31] that, just as it is written, "LET HIM WHO BOASTS, BOAST IN THE LORD." Paul makes two observations about the new Christians in Corinth: 1)  God chooses the weak and foolish things of the world in preference over the strong and wise, and 2) It was God's doing that the Corinthian Christians were in Christ. 
1CO 2:1 And when I came to you, brethren, I did not come with superiority of speech or of wisdom, proclaiming to you the testimony of God. [2] For I determined to know nothing among you except Jesus Christ, and Him crucified. [3] And I was with you in weakness and in fear and in much trembling. [4] And my message and my preaching were not in persuasive words of wisdom, but in demonstration of the Spirit and of power, [5] that your faith should not rest on the wisdom of men, but on the power of God. As in 1 Thessalonians 2, Paul summarizes his ministry in Corinth. Yet these remarks make a strong statment about the message: Jesus Christ and him crucified. 

In manner, Paul reminds his readers of his weakness, fear and trembling.  Though Acts shows Paul reasoning and trying to persuade the Corinthians, the strength of his message was not based upon better debate techniques or clever expressions of ideas. In contrast, he spoke of little more than Jesus and him crucified. 
1 CO 3:5 What then is Apollos? And what is Paul? Servants through whom you believed, even as the Lord gave opportunity to each one. [6] I planted, Apollos watered, but God was causing the growth. [7] So then neither the one who plants nor the one who waters is anything, but God who causes the growth. [8] Now he who plants and he who waters are one; but each will receive his own reward according to his own labor. [9] For we are God's fellow workers; you are God's field, God's building. Paul declares the place of preachers in evangelism: servants through whom people believe he message. 

And here again is the idea that God provides the opportunities for people to minister, and that God causes the growth.
1CO 3:10 According to the grace of God which was given to me, as a wise master builder I laid a foundation, and another is building upon it. But let each man be careful how he builds upon it. [11] For no man can lay a foundation other than the one which is laid, which is Jesus Christ.  Here the foundation of the church is said to be Jesus. In context, this is in comparison to the various ministers who proclaim the messsage. 
1CO 4:14 I do not write these things to shame you, but to admonish you as my beloved children. [15] For if you were to have countless tutors in Christ, yet you would not have many fathers; for in Christ Jesus I became your father through the gospel.  Paul claims that his being the source of the gospel for the Corinthians makes him their spiritual father. 
1 CO 6:9 Or do you not know that the unrighteous shall not inherit the kingdom of God? Do not be deceived; neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor homosexuals, [10] nor thieves, nor the covetous, nor drunkards, nor revilers, nor swindlers, shall inherit the kingdom of God. [11] And such were some of you; but you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus Christ, and in the Spirit of our God. Paul gives an interesting summary of the Corinthians: Though they had been characterized by participation in various sins, they were "washed," "sanctified" and "justified" in the name of Christ and in the Spirit of God. This is probably a reference to their Gentile, pagan standing prior to conversion and their baptisms with the characteristic "in the name of Christ" formula.
 1CO 12:12 For even as the body is one and yet has many members, and all the members of the body, though they are many, are one body, so also is Christ. [13] For by one Spirit we were all baptized into one body, whether Jews or Greeks, whether slaves or free, and we were all made to drink of one Spirit.  In a larger discussion of the members of the body, Paul comments that all Christians have been baptized by one Spirit into one body. He also mentions that baptism was the same for Jews and Greeks, slave or free.
1CO 14:23 If therefore the whole church should assemble together and all speak in tongues, and ungifted men or unbelievers enter, will they not say that you are mad? [24] But if all prophesy, and an unbeliever or an ungifted man enters, he is convicted by all, he is called to account by all; [25] the secrets of his heart are disclosed; and so he will fall on his face and worship God, declaring that God is certainly among you. In the midst of a discussion about the role and relative value of the gift of tongues, Paul maks an interesting observation about how an unbeliever in the midst of the assembly might ome to faith: Through prophesying, he might be "convicted," "called to account" and the "secrets of his heart be disclosed."  Whether this is possible through preaching in the absence of the miraculous gift of prophecy is not clear from the context 
1CO 15:1 Now I make known to you, brethren, the gospel which I preached to you, which also you received, in which also you stand, [2] by which also you are saved, if you hold fast the word which I preached to you, unless you believed in vain. [3] For I delivered to you as of first importance what I also received, that Christ died for our sins according to the Scriptures, [4] and that He was buried, and that He was raised on the third day according to the Scriptures, [5] and that He appeared to Cephas, then to the twelve. [6] After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; [7] then He appeared to James, then to all the apostles; [8] and last of all, as it were to one untimely born, He appeared to me also. [9] For I am the least of the apostles, who am not fit to be called an apostle, because I persecuted the church of God. [10] But by the grace of God I am what I am, and His grace toward me did not prove vain; but I labored even more than all of them, yet not I, but the grace of God with me. [11] Whether then it was I or they, so we preach and so you believed. This text is a succinct summary and restatement of the gospel the Corinthians heard.  Notice the key elements:

1- Christ died for sins according to the Scriptures
2- He was buried and raised form the dead on the third day, according to the Scriptures
3- After the resurrection he was seen by the apostles and some others. 

Paul claims this is what he preaches, and this is what the Corinthians believed.  If they hold to this message, they will be saved-- but if do not, it is possible for them to have believed "in vain" (i.e. disqualifying themselves for the reward).

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