If you want to do something really sobering, go to the probrewer.com forums, and look in the "work wanted" section. You will find hundreds of people with degrees in brewing science or related fields, with internships at good breweries, who can't find work.
Getting in on the ground floor somewhere is good advice, but as was mentioned earlier, you may be the only getting paid, and minimum wage at that. So unless the brewery you're at really takes off and becomes really successful, I wouldn't plan on making a future there.
I'm someone who isn't in the industry, so take this with a sack of salt, but I'd say the best way to get into the business would be to get a business degree, or at least take enough classes and get enough experience in business to be able to start and run your own brewery, and then hire a kid who went to school for brewing for minimum wage to work as your brewer.