Check yourself. Make sure you are not leading your respondents' answers. There may be implicit opinions expressed in how the questions are worded or how the survey is administered. When in person, make sure your body language is appropriate and encourages respondents but does not express an opinion on their response.
Ask follow-up questions during the interview. Ask for details or clarification if the respondent is vague or contradicts themselves. Try to ask similar questions from multiple angles. For example, one question could ask about an organization's priorities and a later question could ask the respondent what they consider to be crucial areas for the organization to address. Similar information (i.e. what the priorities are) should be provided, but from different perspectives.
Research your respondents. If you are performing a survey, look into common responses for a given demographic or group. For interviews, research previous information and views expressed by the respondent. Check to see if common concerns about biased responses arise and ask about them.
Include other information. Check documents relevant to the issue you ask about in the survey or interview. Examples of useful documents include reports, meeting minutes or news stories. Determine if these documents provide a similar account of the facts as the person interviewed or surveyed.
Corroborate with other qualitative research. Instead of relying on a few key sources of information, ask others involved in the issue. Different employees, stakeholders or observers will have views on the issue and can provide complementary or conflicting information. This will help identify bias or unique perspectives for further questioning.