John 20:6-10
John 20:6 (KJB)
Then cometh Simon Peter following him, and went into the sepulchre, and seeth the linen clothes lie,
Peter finally arrived at the tomb but he did not just look in as John did, instead he went right inside the tomb and he saw the line clothes. Now the word “seeth” is not a word in the Greek which means a casual look but the word means “an intense look, study, or observation.” Peter was intently looking at the situation and trying to make an assessment of what had happened. He spent a little time trying to piece together what happened. Maybe he thought he might find some evidence as to who took the body.
John 20:7 (KJB)
And the napkin, that was about his head, not lying with the linen clothes, but wrapped together in a place by itself.
Peter may have been stymied because there seemed to be order in the way the grave clothes were laid out. If it was grave robbers or Romans, the grave clothes would have been in disarray. This is why Peter seemed to be in a state of intense study of the situation. Since the clothes were in order, it would seem that it was a slow removal of the body. Where were the spices that were in the burial clothes? These things would have placed Peter and John in much consternation.
John 20:8 (KJB)
Then went in also that other disciple, which came first to the sepulchre, and he saw, and believed.
Now John decides to go inside the tomb and to see if everything that Peter said was true and once he was inside, he confirmed the fact that everything Peter had said was true. Since there was no body inside, John would not be considered unclean.
John 20:9 (KJB)
For as yet they knew not the scripture, that he must rise again from the dead.
Jesus had told the disciples many times that He was going to be crucified, buried, and then He would rise bodily again on the third day. The disciples had not yet understood these things but when the Holy Spirit will be given, He will bring to remembrance all he things which Jesus preached to the disciples. At this point they were probably bewildered at the disappearance of the body of Jesus as they were not yet thinking on a spiritual level that all these events were prophesied to happen, including the resurrection.
John 20:10 (KJB)
Then the disciples went away again unto their own home.
Since they had now ascertained all the information they could, there would have been no reason for them to remain around the tomb. So they returned to their homes and remained by themselves for the time being. They probably met the other disciples and told them what had transpired. At this point they were probably still laying low.