This is a question that is hotly debated. While the early church set the day of crucifixion on Friday, the biblical evidence for a Friday crucifixion is very weak. The reason for setting Friday as the day comes from this verse: "And now when the even was come, because it was the preparation, that is, the day before the sabbath..." (Mark 15:42).
On the day before every Sabbath was a day of preparation so no work would be done on a Sabbath. The early church understood this to mean the weekly Sabbath (Friday sundown to Saturday sundown) and, since Jesus was crucified on the day of preparation, they assumed it must have been on a Friday afternoon. The error in this logic is that the Sabbath referred to in Mark 15 was the Feast of Unleavened Bread. This is the Feast of the Passover in celebration and remembrance of the Israelites being delivered from Egyptian bondage.
The Feast of Unleavened Bread is set on Nisan 15 (Leviticus 23:6) and it is a High Sabbath (rest), also called a High Day:
"The Jews therefore, because it was the preparation, that the bodies should not remain upon the cross on the sabbath day, (for that sabbath day was an high day,) besought Pilate that their legs might be broken, and that they might be taken away" (John 19:31).
John 19:31 tells us that this was before the High Day Sabbath of the Feast of Unleavened Bread. Therefore the day before the Sabbath, the day of preparation for the feast, is Nisan 14. Since the Passover feast is set according to the calendar (unlike the weekly Sabbath that is set according to the day) Nisan 15 could fall on any day of the week.