I start this chapter on Easter morning, 2012. Today I and Christians all over the world will celebrate that Sunday so long ago, perhaps in the year AD30, when Jesus physically emerged from the tomb in which they had buried him. For Christians, every Sunday is a little Easter, a little celebration that Jesus has risen from the dead. 
We say it was after three days, because the Jewish day goes from sundown to sundown. Jesus was thus dead from about 3pm to sundown on Friday (day one). He was dead all Saturday (day two). Then he was dead from sundown on Saturday to the time when he rose early Sunday morning (day three). 
Most scholars believe he was buried in a vault something like this one, today located in the Church of the Holy Sepulcher not far from the traditional site of Jesus' burial.
There is another site, Gordon's Tomb, which is located in a garden today and has a rock outcropping that looks somewhat like a skull. Many Christian visitors say it gives them a better feel for what they picture when they read John 19:41, even though it is not likely the original location. 
The earliest report of Jesus' resurrection comes from Paul in 1 Corinthians 15:3-7.  Since Paul wrote this letter around the year AD54, it is a very early report indeed, likely within fifteen years of the event. Paul says that he himself inherited this tradition (15:3), presumably from people like James and Peter in Jerusalem (e.g., Gal. 1:18; 2:9).
It is not at all likely that he is lying, since he has enemies in the church at Corinth and indeed had conflicts with the Jerusalem church. Both groups no doubt would have loved to show him wrong if he was saying false things about such a fundamental tradition. But we have absolutely no evidence that anyone did. It is thus overwhelmingly likely that the tradition Paul passes on here is exactly what everyone in Jerusalem was saying.
Paul doesn't give much detail. He basically gives a list of those to whom Jesus appeared. Jesus rose on the third day (1 Cor. 15:4). He appeared to Peter and then to the Twelve (15:5).  There was an appearance to a large group of over 500 people (15:6). Then there was a second wave of appearances. Jesus appeared to his brother James and to all the apostles (15:7), ending with his appearance to Paul himself (15:8).
These were all real people, most of whom were still alive at the time Paul was writing. We have good reason to think that many of them suffered considerably in consequence of this belief. The disciple James, Peter, James the brother of Jesus, Paul--all of them were put to death, still firmly believing that they had seen Jesus alive after his death. It is not reasonable to think these individuals were lying...
 The Bible nowhere equates Sunday with the Jewish Sabbath. The Jewish Sabbath was from sundown on Friday to sundown on Saturday. For Christians, Sunday is a celebration of Jesus' resurrection. For this reason, those who choose to give up something for Lent do not have to do so on the Sundays of that period. No Sunday is a day for fasting.
 Being dead three days also makes a symbolic connection with the prophet Jonah. Jonah was in the fish for three days and three nights (Matt. 12:40).
 Although the Church of the Holy Sepulcher is currently within the walls of Jerusalem, archaeology has confirmed that it was right outside the city at the time of Jesus. The Romans usually crucified right outside city walls on a path where people would walk by.
 It would be very common to think that the gospels were written first because they treat Jesus, who came before Paul. But the gospels were not written by Jesus or at the time of Jesus. They were written later in the century, likely after Paul was already dead in fact.
 This would not have included Judas Iscariot at this point. Either "the Twelve" is used loosely or Paul has in mind those who would be considered the Twelve after Judas was replaced.