You can now read about how Tom Holland got his role as Peter Parker at The Daily Beast.
Some of the more interesting quotes I found from that article were these.
It’s not The Dark Knight,” he says. “One of the special things about what we’re going to try and create is that you’re going to see the biggest independent film ever. It’s not going to be an epic thing; it’s going to be a film surrounded by these incredible things, but that follows this boy and his life. Peter Parker is a favorite of many because everyone can relate to him, and we’re going to try to make everyone relate to our Peter Parker. And John Hughes is a perfect example of what we’re going to try and do.
“We had to do a movement test and then I said, ‘Can I just demonstrate some of the things that I can do?’ and they all were a little unsure of what I was talking about, and then I did a series of backflips and landed on the X, and was like, ‘Thank you!’ and then just left.”
He first did five self-tapes and then had two auditions; one with Robert Downey Jr. and another with Chris Evans which is were he showed off his moves. He did the self tapes with - among others - John Bernthal who is the Punisher on Daredevil. He also learned that he were cast as Spider-Man the same way as everyone else, online.