There’s an endless amount of resources out there for an aspiring publisher, but a good place to start is The Society for Young Publishers‘s advice on how to get into publishing: How do I get a job in publishing?
Remember to ask yourself where in publishing you want to work (Marketing, Sales, Design, Editorial Commissioning, Production, freelance copyeditor, etc.) and keep an eye on @jobsinbooks for what kind of skills those job ads are looking for.
Other recommended reading to get an overview of the industry:
Inside Book Publishing by Giles Clark Hall, Angus Phillips
How to Get a Job in Publishing by Alison Baverstock, Susannah Bowen, Steve Carey
Publishing: Principles and Practice by Richard Guthrie