It all depends on how much you get to talk to the client.
First things first - Ask them to describe their situation at the completion of the successful project with a focus on the systems you are going to tool around with. That is a great place to start because its gives you a feel for their expectations. And it helps you start to define criteria for success.
The second point is that at the beginning of the discovery process you need to ask a lot of open ended questions to get them talking. Later on in the late part of the discovery process your questions will be closed (with simple yes or no type answers.) This is where they are veryifying that you have correctly understood their problem and articulated the right sort of requirements for them.
Don't forget the ubiquitous 5 Ws (What, Where, When, Who, Why) and the H (How).
There is also a technique called the 5 Whys which is good for digging depper into issues.
There is a lot more in this topic, but there are some braod tips for you.