There's quite a lot of literature in the sphere advising boards and staff on searching for new board members. The most common recommendation: seated board members should tap their network. On this matter, I suggest a step further and not to directly seek board members but seek committee or task force volunteers and provide the opportunity for the organization and the individual to mutually screen.
That said, what I don't see so much about is advice for the recruit -- what questions should they ask when considering nonprofit board service? Here's some questions I would ask:
what is the organization's mission, values and is there some kind of strategic plan?
who are the current seated board members?
how often does the board meet and what happens at meetings?
what is expected of a board member in terms of time, duties, money?
how long is board service?
what do I really bring to a board?
Have you other questions you might ask?