If you want your search to be confidential, do not post your resume on public career boards/sites.
Consider going through a Recruiter: This is one reason why Recruiters exist. Going through a reputable recruiter (or 2) ensures complete confidentiality. Recruiters are not suppose to present you a company without your permission and they keep your information confidential. That's their job to do so.
Do your own search: You can also search for positions on your own, but that's more of a reactive job search. You want to include proactive techniques in your search. In other words, rather than finding the position and applying to it online, start with first identifying 10 to 20 companies that you want to work for based on your personal criteria (i.e., less than 10 miles from home, their involvement in the community, the size of the department you'd be working in, their reputation on sites like glassdoor.com, etc.
Build Your Proactive Job Search Strategy: Now that you know WHO you want to work for, now you can determine WHO you need to build rapport with at each company and dedicate at least 90 days to the process of reaching out to people at that company that are either decision makers or influencers. LinkedIn.com is a perfect tool to use for this. If you take this approach and focus at least 90 days to 4 months on it, natural attrition will likely occur in the department: someone will quit to relocate with a spouse to a new city, someone will get promoted, someone will get fired, maybe even a female employee will elect not to return back to work after being on maternity leave. When any of these situations occur, you want to already be TOP OF MIND.
If you wait for the position to be posted, you're several weeks behind because that hiring manager starts first with his/her inner network to try and get referrals before posting it online. By the time it's online, it's usually been open for several weeks. You want to get into the game as close to when the position became available. There's no better way to do that than to start building rapport with the people who have the influence or authority to hire you before the position even shows up on the internet.