My blog title is a good question if you think about it. How did the Apostles come to the knowledge of the things that happened to Jesus when he was all alone. For example; how did they know Satan tempted Jesus in the wilderness (Matthew 4) or what Jesus prayed when he was alone or the content of his conversation with the woman at the well? Did they make it up? I don't think so. In fact I think there are three possible ways the Apostles could know about Jesus' private moments.
1) The Holy Spirit inspired them. This is, in my opinion, the best explanation. Jesus promised the apostles that they would receive the Holy Spirit in a special function to help them carry out their special ministry. He promised that the Holy Spirit would lead them into all truth (Jn 16:13). This can't be a promise for all Christians. If so then we should fire all the Bible teachers, stop having preachers in our churches, and shut down all Bible colleges. No Christian should ever disagree if the Holy Spirit leads us all into all truth. But that isn't what this verse is promising. Of course skeptics will reject this one right off the bat as a "convenient" explanation. I can see their point. BUT if Jesus really did rise from the dead then miracles are possible, God is real, and the inspiration of the Holy Spirit is at least possible. So then, they cannot presuppositional reject this option.
2) They received the information from others. Luke says that he "carefully investigated" everything (Luke 1:3). Therefore, he could have spoken with the Samaritan woman (Jn 4) and others to receive the content of Jesus' private conversations.
3) Jesus told them about it later during his ministry or right after his resurrection. Jesus spent a lot of time with the 12 disciples. It is not a long shot to believe that he later explained to them what happened while he was in the wilderness being tempted by Satan or about other events. We know that after his resurrection he spoke to them "about things concerning the Kingdom of God" (Acts 1:3). So why would it be far fetched to think one night as they sat around a campfire that Jesus explained to them what he prayed about while alone on the mountain or the content of his conversation with Satan in the wilderness? We tell people all the time about our private moments.
Therefore, we have multiple ways in which the disciples could have come to this private information. Can you think of any others?