Meetings with faculty are important and, when well managed, often very helpful. Despite this, Ph.D. students get little direction on how to approach meetings with faculty. Here is my sense of the how to get the most out of faculty meetings, largely focused on early stage meetings in which a potential research idea is being discussed.

It is important that you think about what you want to get out of a meeting. When I meet with a student the first question I ask is some variant of "what is the objective of this meeting?". Always have a clear answer to that question.

A meeting without a written document to discuss is unlikely to be productive. Especially early on, you should aim to have prepared a 4-6 page research proposal (written using LaTex) before asking for a meeting. You should have answers to the following questions:
i) what is the research question?
ii) why is this interesting/important?
iii) how does this project contribute to the existing economic literature?
iv) what is the current state of the literature relating to this project?
v) what industry are you thinking about?
vi) how does that industry work?
vii) have other people worked on this industry? what have they done?
viii) what data is available?
ix) how do you plan to structure an answer to your research question?
x) what kind of model do you have in mind?
xi) (if emprical) what is the basic empirical approach you have in mind? reduced form? structural? a mix? what are the steps that you think might be involved?
xii) how does the data fit in with that?
xiii) what are the likely challenges that you think you will confront?

You don't need perfect answers to these questions. But you do need to have thought about them enough so that you are able to maintain an informative, constructive, half-hour conversation. The best way to make that half-hour productive is to write up a document that describes what you have been thinking regarding these questions. It is important that the document reflect some serious thought, consistent with roughly a week's diligent work.

Unless you have worked through these questions in written form, my experience is that meetings are usually unproductive. Usually my response to requests for a meeting that are unaccompanied by a document, as described above, is to ask that you to prepare such a document before setting a time and date for a discussion.

This is what I do before I pitch an idea to a colleague. It is a good habit to get into early on in your career.

Most of my research ideas are pretty bad. Don't be afraid to have bad ideas. Learning to tell the difference between good and bad research ideas is an important skill to develop. Sometimes an idea that you think is bad has merit that you missed; similarly something you think is good may be terrible. Writing them down, and then discussing them with someone else is the best way to tell the difference. In my experience, roughly 50% of ideas die as I write them up. Conditional on making it to written form, another 50% or so die when I discuss them with someone else.