The stakeholders know their clients, their staff, the community that they serve, current problems they are having, and they also have some ideas for solving those problems through design.
They also have much 'latent' knowledge, or implicit knowledge, of their needs. Details they don't know they know, assumptions so deep they aren't aware they are assumptions. It is your job to elicit the explicit and implicit information through interviews, observations, and background research.
Your time is often limited with your stakeholders, so you have to be efficient. This means you need to be organized. Understand what you need to find out before you start and make sure the questions you ask or observations you make reflect those needs. The questions themselves should be open ended to allow stakeholders to expand on their answers.
While you listen to answers, think of follow-up questions. Anything you don't understand...don't assume, ask! Using recording devices (audio/video) can help keep your brain free to listen and follow up questions. Having one team member take notes also can free up the questioner to focus on asking.
Finally, check for understanding. As with the classic 'explain how to make a peanut butter sandwich' activity, what you hear isn't always what the stakeholder means. Restate their answers to confirm their meaning.
You can get more information from the client through reading about them.
Ask for documentation from the company...mission and vision statements, values, marketing information
Find out about the company using business databases and financial statements
Learn about the community and potential consumers
Personas are a tool to describe archetypes of users, they can be vivid ways to communicate to stakeholders the typical users or uses of a product. For example, typical users of a library could be a 'newly minted assistant professor,' 'liberal arts major with loud roommates,' 'end of career expert researcher.' You develop the personas through research, based on observations/interviews of typical behaviors, desires, or needs.
Here are useful resources to learn why and how to create a persona:
Personas - User Focused Design by 
User-Centered Agile Methods by