When introduced to a new domain I find the best approach is to look for overall models/patterns/themes to understand the new domain. Test the models by asking questions and interpreting what the model would indicate.
Once you have a good model you can make predictions about the domain. These predictions you can run by the client. This shows clients you can figure things out about the domain instead of just recording what they say.
Over time, you will learn there are many models that apply to many different domains. Once you know a model that applies, you can learn a lot about the domain very quickly.