Jobs at small Omaha companies nobody posts about - any advice?

A friend who works at a local manufacturer says there are openings not advertised online. There are 6 people counting on me, so I am trying to be careful. They like a brief email with a résumé. What do you write in a cold email?

A short email with two sentences about what you can do and your résumé attached worked for me. I followed up after a week.