Although this is not an exhaustive list, the following tips should help you achieve your goal:

1. Appoint a culturally diverse search committee. Use the search committee to recruit, not just screen applications.
2. Develop a clear and unambiguous position description. If diversity is related to the mission of your organization, then it should be reflected in this position description. Review the description by asking yourself, "What is there in this description that would make it more or less likely that my desired candidate would apply?" Gear the description to the audience you want to attract.
3. Develop a matrix of required and preferred requirements. Make sure they are job-related, and that diversity is reflected. If diversity is not a job-requirement in some way, then the committee cannot use diversity as a hiring criterion.
4. Make sure the position is circulated in culturally diverse communities, and advertise in markets that have a highly diverse audience. Don't just sit and wait for your candidate to apply. Go out there and invite applications from the people you want to be working in your organization!
5. Evaluate applications purely by the matrix you developed before looking at any applications. This is key to giving everybody a fair shake and decreasing the influence of your unintended "culture schemas." Discuss the qualifications with the search committee so that everyone knows the range of acceptable behavior that meets the culturally neutral job qualification. When looking for strong leaders, for example, you may find that women have different kinds of leadership experience than men do. Do not screen out desirable candidates because you narrowly construe the qualifications.
6. Make all candidates feel welcome. Treat all interviewees the same; as individuals with unique needs and interests. Ask all interviewees if there are particular co-workers or community groups that they would like to meet with during their visit in order to address individual matters. Some people might say they want to talk to local school groups while others want to meet with members of the local Hispanic community. Give the candidates the chance to confirm that they will feel welcome in this community over the long run.
7. Abide by all federal rules regarding the appropriateness of the questions you ask of candidates.
8. Hire the best person! In addition, make sure that all those you don't hire speak of you, and your process, well. They are ambassadors for your business/agency, and may steer future hires your way.
9. Aside from the search process itself, consider developing intern programs to reach out to unrepresented cultural groups of interest.