Once you've solicited responses, you may want to follow a multi-step process in selecting candidates. The Neighborhood House Charter School process described above is one model. Once you've selected applicants to interview, take care in preparing a list of interview questions that will tell you what you need to know about a candidate. You may want to do two interviews, an initial screening interview and a later, more in-depth interview. Checking of references can happen between the first and second interviews.
MACS can provide lists of sample interview questions.
As Eric Premack suggested, it's important to bring someone into the process who has experience in making personnel decisions. You may want to have a hiring committee of three or more so multiple interviewers can compare their impressions. Especially if you're interviewing a large number of candidates, taking notes during the interview is important and will help in making decisions later when you have many applicants to compare. If at all possible, it's good to see a teacher candidate in action before making a final hiring decision. Or, if your school is already up and running, you could invite the candidate to guest-teach for a small portion of the day.