Best of luck in your application!
There are about 15 breweries in my area, and I'm very active in the craft beer community, so I'm friends with most of the brewers around town. I'll tell you from my experience that the BEST way to get a paying brewery position is to volunteer at a brewery or two first.
One of the larger local breweries recently had an assistant brewer position open up, and they received about 30 applications. Of those 30, only 8 had prior professional brewing experience. The job ended up going to a guy who had learned a ton about brewing and the business (this is key) through about 18 months of volunteering at two other local breweries, followed by a assistant brewing position for 6 months at the second brewery he had volunteered for (a small microbrewery). This is the typical path for about 80% of all entry level brewers. The other 20% go through a program like Siebel. I've never seen a homebrewer transition straight to a professional brewing job unless they started their own brewery.
Also, like some others said, be prepared to make very low wages. Expect literally about $8-9 an hour as an assistant brewer, and may only get part time hours. Most of the head brewers at the microbreweries here make about $26-28K. Neither get benefits of any kind. You really have to move to a big regional or statewide brewery before you make any money.
Hope that gives you some good information, and best of luck in your endeavor!