We have only two main sources on the resurrection of Jesus: the writings of Paul, and the Gospels. Let’s look at each of them in turn.
Paul, to our knowledge, never met Jesus before his death. His experience of the risen Jesus seems to be like a vision, and he describes it differently in different places. He rarely talks of the specifics of Jesus' life, or of the specifics of his resurrection, but he talks at great lengths about the spiritual significance of the resurrection. Paul may be a good source for information on what many early Christians believed, but he is not a good source of evidence that the Resurrection was a real event in history. Everything he says either comes from a vision or is hearsay, handed down from the apostles. Unfortunately, we don’t have any writings that we know are written by the apostles, so we can’t even know if Paul is representing them accurately.
Next, there are the gospels, which do go into many specifics on the death and resurrection of Christ. Unfortunately, all four gospels are anonymous and un-dated. We don't know when, where, or by whom they were written. Most scholars believe that Mark was written first, between 67 and 70 AD, with the rest of them spanning 10 to 30 years after. All the information we have about who wrote the books comes from later, oftentimes shaky, tradition.
It is very likely that the authors of Matthew and Luke copied large portions of their gospels from the author of Mark. There are some very close similarities between the books. For instance, when one looks at Mark 13:14 and Matthew 24:15 it is hard to see how those passages could have been written independently of each other.
At this point almost 2000 years down the road, we have no real way of knowing how trustworthy the gospel authors are, or if they talked to eyewitnesses at all. All we can do is try to read between the lines to determine what happened.
The problems with the resurrection go even further than what is indicated above when we look at the culture that produced them.
Miracles and supernatural entities were an accepted part of life. Literacy hovered around 5%, so it was much harder to propagate reliable information. Science and the scientific method didn't even exist. We have no way of knowing what it would take to convince the people back then that a miracle had occurred, but it would probably have been a lot less than it would to convince someone of that same fact today.
The sources we have are also limited in that many non-Christian sources have been destroyed. We know from many of the early church fathers that such sources existed because they wrote about them, but we will never know what they said. Every single substantial source we have regarding the resurrection of Jesus fall into one of two categories: Texts written to convince people to be Christians or to defend Christianity, and texts written to comfort and exhort people who already were Christians. Unlike what we would see in a modern law court, we will never know the other side of the story.
If somebody today was to claim that Elvis rose from the dead, and they were to base that claim on a bunch of letters and papers by authors we know nothing about, would we believe them? Would we not request evidence? Doctors reports, video footage, something to back up the incredible claims we were reading in the texts. After all, people don’t just rise from the dead every day!
Jesus’ resurrection can easily be explained by legendary embellishment, religious experience, and writers who wanted to tell a beautiful story or to use Jesus to make their point.
There is just so much we will likely never know about what happened all those years ago. It would be unreasonable to believe such an extraordinary claim based on such flimsy evidence.