The uniqueness of each candidate and interview will help determine how to approach reference checks. However, you may want to:
Confirm items on the candidate's resumé, such as past employment dates and positions; accuracy of claims about achievements; competence; superior/subordinate relationships; circumstances of leaving past jobs.
Use open-ended questions about the candidate's strengths; weaknesses; contributions to the organization; most valued qualities; decision to leave, and its impact on the organization; relationship to bosses, peers, and subordinates.
Encourage elaboration of explanations with questions such as "Can you explain that?" or "Can you tell me more?"
Follow up on any hunches about the candidate that you may have developed during the interview.
Ask the referee if there is anything significant you have missed asking about.