Again, Eric makes excellent points. His suggestion about gaining some experience with a design house or consultancy is good, if that is possible in your situation. In any case, I agree with his comments about relationships with clients.
On a larger project, it is sometimes in both party's interests to propose a 2-part contract: a fixed price study subproject with a deliverable of a formal recommendation report, followed optionally by the main project defined in the first part.
With this do you mean the client would pay for an evaulation of their requirements to determine a course of action (and the results of said study) and then pay if the work is done?
Actually I have never personally tackled a big enough assignment where I could propose a 2-part contract, but I know how it generally works. The way you pitch it is something like this: "In order to make a responsible recommendation to you, I need to spend some time studying details of your operation and requirements. As you will understand, I'm sure, I can't afford to do this just for speculation, so what I'd like to propose is that I will spend [X amount of time] with you [or your staff, where that is appropriate] and deliver to you a thorough written analysis of your problem and my plan of implementation, as Part I of our agreement. I will charge you for that amount of time. The plan of implementation will include a proposal for the timing and your cost for me to complete the work described in that plan." In other words, they pay you for Part I, so you're not wasting your time, and they get a look at how you see the project, as well as a cost estimate. Naturally, you won't reveal enough details so they could pick up the plan and execute it themselves. If you succeed in impressing them, it should be a good basis for them to approve Part II, as described in your Part I document. Now this isn't appropriate for a simple web design project, it would only be used for a fairly major project, probably one where you would need to call in some others for certain parts, as Eric described. The concepts are: splitting off the study (R&D, if you will) part and defining a "deliverable"--what you promise to deliver for a price; and, once again, looking at it from the client's perspective: for a rather small known cost, they can get a formal analysis and a well thought through cost estimate for the entire project. One of things every business hates is uncertainty. This approach helps the client by limiting his investment until he has something more than just an interview to go on. He has the option to reject your plan and only pay the amount agreed on for the report. You might charge a client just a few hundred dollars for such a report, which isn't a big amount for most businesses you're likely to deal with. For this, they get a document that demonstrates that you understand their problem and have a professional plan for how to solve it (but not with such innovative, detailed descriptions that they can easily have someone else execute it). It should give them more confidence in your ability to execute your plan. And they will have a cost estimate based on reasonable knowledge of the scope of the work; again, eliminating uncertainty.
Nearly every opportunity is unique, so "one size" definitely doesn't fit all! But that's one potential approach for a large and poorly defined project.