Our chief sources of information about the Apostle Paul are (1) several of his own letters, preserved for us in the New Testament, and (2) the account of him given by Luke in the book of Acts.
One naturally asks whether we can be sure that the letters attributed to Paul are in fact his. A partial answer is that a forger would run into difficulty. If he wrote a letter, say, to the church at Corinth during Paul's lifetime, and signed Paul's name, the Corinthians would naturally mention it the next time they sent a message to Paul, and Paul would naturally reply: "What are you talking about? I never wrote anything like that!" If a letter supposedly to Corinth were circulated after Paul's death, sooner or later a copy would reach Corinth, and the members of the church there would ask, "If Paul wrote this letter and sent it to us while he lived, how does it happen that no one here has ever heard of it?" Thus, it would be difficult to obtain credence for a forged letter to a congregation. This argument does not apply to a letter to an individual (such as Timothy or Titus). Moreover, it arguably does not apply to the Letter to the Ephesians. Although some ancient copies of this letter begin:
Our other source of information is the book of Acts, where Paul (at first called Saul) appears in 7:58-8:1; 9:1-30; 11:25-30; 12:25--28:31. Here we read how Paul at first opposed and persecuted the Church, how he had a vision of Christ and was converted, and devoted the rest of his life to spreading the Gospel of Christ.
Portions of this account include statements like "we then crossed over to Troas," which are taken to mean that Luke was a companion of Paul for part of Paul's journeys. Since these accounts, particularly those of the shipwreck on Paul's last voyage, show every sign of being accurate eyewitness accounts (see the book THE VOYAGE AND SHIPWRECK OF SAINT PAUL, by James Smith of Jordan Hill, FRS) and since a comparison of the style of various portions of the book of Acts makes it highly improbable that it is a scissors-and-paste job, with portions of one man's work inserted into a story by someone else, many scholars consider the claim that Acts was written by a companion of Paul to be well established.
On the other hand, it is not always clear how the chronology of Luke's account of the life of Paul is to be fitted with the autobiographical snippets we find in Paul's own writings, and for this reason some scholars dispute the genuineness of the book of Acts.
For an old but still worth-while introduction to the subject, and a defense of the conservative position, I refer the reader to A HISTORICAL INTRODUCTION TO THE NEW TESTAMENT (the title varies a bit from one edition to another) by George Salmon, FRS. A portion of this book (dealing with the authorship of the Fourth Gospel) can be obtained by sending the message GET JOHN PART2 to the address LISTSERV@ASUVM.INRE.ASU.EDU