It's very important to find out as much as you can about their business. For example:
Whats your target market?
Where do you currently get most of your business from?
What other methods are you using to promote your business?
How do you perceive your business within your industry? (reputable? well known? reliable? the best?)
Then you can ask a few more specific questions relating to the site:
What goals do you have for your site?
What end results would you like your site to achieve?
(You can also prompt them a bit. For example, Are you aiming to directly increase sales, to generate leads/enquiries or mainly to increase branding and awareness?)
Asking these general questions is an important stage as it shows that you really do care, and then you can come up with a plan of attack suited to their goals and objectives.
Once you have an idea of what they want the site to do, then you can ask even more specific questions when the time is right. Such as:
Do you need any specific functionality?
Is it important that your customers are able to interact with your site?
Do you have content prepared that we can use on the site?
Will you be using your existing business colour scheme?
What type of theme would you like? (corporate, professional, funky, cute, clean etc.)
There are plenty more questions to ask, thats just a brief idea. The most important thing, as said above - is show that you care, and REALLY listen to the answers they give you as this will help immensely.