Being as you have only your homebrew knowledge, I would skip the resume unless they ask for one. Visit the breweries, meet the owners, managers, brewmasters. Get to know them. Bring your passion and arm yourself with good questions. Show them your willingness to learn.
Example:
I was working a dead end job a few years back and really wanted to pursue a career in automotive customization and fab. I had absolutely zero experience. After finding out what it would cost to send myself to a trade school,I decided to see if anyone would hire someone as green as me. Why pay for school when someone might pay you to learn right? I visited all the shops within a 90min commute that did the type of custom work I was into. I found one that wasn't actively hiring, but considered all applicants. They were actually happy I didn't have experience. Said that it was less bad habits they would have to break and they could teach me their way. I got the job. They paid me minimum wage at first(a huge pay cut for me at the time) but re-evaluated my progress frequently and soon the money was good.
Be polite, be confident, be inquisitive, and most of all be persistent.