Obviously I have missed out on going this year, but I would love to go next year to watch the auditions, does anyone know how this is done? Maybe even tickets for shows after the auditions would be great!

You apply online to Applause Store.

I would have said that

Applause Stores as aforementioned

And bear in mind that they send out more tickets than there are places in the theatre, so even if you get a ticket, it's no guarantee of getting in.