1. What do you love most about the industry your business is in?
In my five years of so of helping businesses through design, I have learned that I like listening to like minded people talk-and since people like to talk about themselves-asking such a question like this does a few things for you and your client. Firstly, it shows the client you are interested in who they are, that you are an empathetic person, and not some machine who pumps out logos. Secondly, this information can actually really valuable, for example, in a situation where the client you are helping is the brand of the business you are designing for. Write down most things the client tell you-they are not talking for no reason.
2. Can we create a build of your ideal user?
Understanding the client's ideal target audience is incredibly helpful when designing, since after all, you are designing a product that the target audience will be interacting with and experiencing. If your design does not end up being a reflection of both the business as a persona and the businesses target audience, then some rethinking is in order.
There are a couple of ways you can make sure that your design comes out a likable and relatable product to that of a businesses target audience. A prototype can be shown to a study group (that is hopefully the same people as the target audience) and feedback can be recorded. Another more practical way is to try and get into the mind of the ideal user and to empathize with them.
It shows the client you are interested in who they are, that you are an empathetic person, and not some machine who pumps out logos.
3. What are your current and end goals?
Design can be considered a vehicle to help a business reach their goals, both short and long term. By asking these questions almost verbatim to get a simple and concise answer, you are taking another step forward in the client's ideal direction. However, like all questions you ask, studying their response after the discovery call to get a better understanding is what truly leads to a clear path and better design.
4. Who are your competitors?
Competitors always need to be understood. If two brands in the same or similar industries are too close in visual style, huge problems occur, so the importance of taking into consideration the surrounding competitors cannot be understated. A client's answer to this question should include competitors in both their region and industry that are at a similar scale to theirs. This question in particular can open up an entire conversation about market positioning.
5. How do you want to be similar and/or different from your competitors?
Although the visual similarities and differences should only be touched on, this question is mainly pertained to how the brand you are designing for wants to be seen and heard by their customers in relation to their competitors. Hopefully the client chooses competitors who have very compelling brand feel, tone of voice, impact, etc. to be similar as, and if not, some guidance in the right direction is in order.
The visual similarities should only be talked about relatively briefly, but understood to the point that there is mutual agreement between client and designer since the client is (probably) not a graphic designer themselves. This is where your expert level design knowledge comes into play. Explaining, not just now, but at almost every phase of the design process, what is most visually effective and why it is most visually effective to the point that the client gives away almost 100% creative freedom is the goal.