I submitted a CV, cover letter and portfolio to Penguin Random House through their careers website. I heard back a few weeks later that I had been selected for interview and went to their London offices. I met with a lead designer for the children's section and another designer who was previously a design assistant. It was a pretty informal interview- I talked them through my portfolio, answered various questions about my experience, got to have a look at some of the books they were currently working on etc. I also had a chance to ask them questions at the end. They said there would be a second interview with higher up members of the team should I be successful at the first interview stage. I heard back several weeks later that I hadn't got the job, there was a little in the way of feedback too which helped.