New American Standard Bible 1 Samuel 13:1
Saul was thirty years old when he began to reign, and he reigned for forty-two years over Israel.
The words "thirty" and "forty" are not in the original Hebrew.
Berean Literal Bible Acts 13:21
Then they asked for a king, and God gave them Saul son of Kish, a man of the tribe of Benjamin, for forty years.
King James Bible is not as definite about the 40 years:
And afterward they desired a king: and God gave unto them Saul the son of Cis, a man of the tribe of Benjamin, by the space of forty years.
Gills explains them this way:
The Jews are very much divided about the years of Saul's reign, some allow him but two years (x), and others three, one year that he reigned with Samuel, and two by himself (y), which they conclude from 1 Samuel 13:1 but others (z) think this too short a time for the things done by him, the wars he fought with many nations, and his persecution of David from place to place; wherefore others (a) allow him, some seventeen, and others twenty years; but our apostle ascribes forty years to him, which must be understood both of him and Samuel; with which Josephus (b) agrees, who says that he reigned eighteen years, during Samuel's life, and twenty two years after his death, ...
That explains the 40 years in Acts.
from the beginning of Saul's kingdom, or from the time that he was anointed by Samuel the prophet, until the kingdom was renewed to him by all Israel, was one year, and then Saul chose three thousand men out of Israel after that he reigned two years by the consent of all Israel, until he sinned in the business of the Amalekites, and then he was accounted as a dead man, and the years of his reign were not numbered; at which time David was anointed
That explains the 2 years in 1 Samuel 13:1.
(x) Seder Olam Rabba, c. 13. p. 37. Juchasin, fol. 11. 1. Kabbala, R. Abraham, &c.
(y) T. Bab. Temura, fol. 15. 1.
(z) R. Levi ben Gersom & R. Isaiah in 1 Samuel 13.1.
(a) Shalsheleth Hakabala, fol. 8. 1.
(b) Antiqu. l. 6. c. 14. sect. 9.
How long did Saul reign for?
This is a messy one depending on how one interprets "reign". By our modern standard, a reign of twenty to twenty-two years is reasonable.