For a site with such narrow scope, I’d start by contacting local businesses and ask them to advertise on your site. If you haven’t sold sponsorship before, talking to business owners where you already shop in will help you understand what they expect to get from their spending. My experience selling promotional material taught me that every business owner has a different expectation.
You better start getting data about your site (quantity of readers over time, demographic, etc that you can gather from tools like Google Analytics) and details of what you’d like to offer in exchange (banners? sponsored posts to a blog? other type of featured content?) and at what price.
There are books on the topic, too. Your local public library may have some useful resources too. Start reading and keep on updating this topic as you learn and experiment more .