Don't wait for job ads; schools frequently just dip into the "adjunct pool," and don't need to advertise for adjuncts. So your aim is to get into the pool. You do that by sending (or emailing) your CV and a cover letter that lists specific courses you'd be interested in teaching to the department chairs.
This. It's important to include the list of courses you can teach--and be honest. If you say you can teach it, you'd better be able to follow through, if they offer you the opportunity.
I started adjuncting at MyCity U when I was still a doctoral student, so they knew me and knew what I could teach. I got my current gig there through my former doctoral advisor, who was retiring and knew that I could teach his course--a particularly difficult course to teach online. The associate dean (whom I knew, but not well) interviewed me about the challenges of that course, liked my answers to his questions, and has hired me most semesters for the past several years as a result.
But I just landed a new gig in Somewhere Warm doing pretty much what zharkov recommends. Because the CC in Somewhere Warm has a lousy website (pretty, but very little info), it wasn't clear who the department chair or department faculty were, so I sent an email to the director of HR asking whether we could meet (so I could learn more about the school, etc.). I included within the email a list of courses I could teach, and I attached my CV. He blew me off, saying he didn't have time to meet with me. But two weeks later, the department chair emailed me and asked me whether I could cover two courses. The only way she could possibly even know I exist is through the HR director. I've just received the new-hire paperwork, and I'll have three or even four sections to teach this spring, on top of my MyCity gig (which is online only). And it turns out that she may have a full-time position available next year (although I don't know yet whether it would be TT), and she seems to be hoping I'll apply for it.
So, yes, zharkov's method works.