This is one of those few passages that would be possible to challenge it's accuracy - why you may ask. Well all three accounts specify that only Peter James and John were there with Jesus, and that's few enough people that they could have made it up. However do bear in mind that often the statement of one person is enough to convict someone in court, so that of three would be considered fact by many.
In this passage Jesus and the three disciples go up a mountain to pray, Jesus then becomes a brilliant white and Moses and Elijah appear with him (I'm kinda curious as to how the disciples knew who they were - did they recognise them from pictures? or did God just tell them?). Peter does his usual trick of open mouth and insert foot as he offers to build shrines for each of them. This I am assuming would take some time, so I also assume that Peter thought they were going to stick around for a bit. I wonder what he thought they were going to do? Anyway at this point a cloud appears and God speaks from it telling them:
"This is my beloved Son, and I am fully pleased with him. Listen to him."
This is the second time God has done this the first was when Jesus was baptised. Then Moses and Elijah disappear and Jesus instructs the disciples to not speak of what just happened, until he rises from the dead. So they didn't except for amongst themselves, and that was mainly to discuss what "rise from the dead" meant. Finally Jesus tells them that the religious leaders are correct to say that "Elijah must come before the Messiah" - but that he has already done so and suffered at their hands, the disciples then finally realise that he is referring to John the Baptist.