My recommendation to entrepreneurs embarking on customer discovery is to watch a few hours of Law and Order. The original, not the derivative work.
See, I've traveled about 150 days a year for the last 10 years of my career. My Sunday afternoons "resting" on the sofa turned into binge-watching Law and Order on TNT. I've since learned that it was in fact not very good for my body and soul, and I stopped binging. But not before I realized that Law and Order has a lot in common with customer discovery. Customer discovery is the process of interrogating the market to understand the problem, who the problem affects, and who is willing to pay to solve the problem. The keyword here is "who" -- who is a person, not a company. All this work helps identify your ideal customer through establishing a common set of characteristics and traits. Simple… right? Not simple at all. But Law and Order can make it a little easier.
And here's why: you know that dance that Sam Waterson and Jerry Orbach always do? The one where Jerry believes that he's found the perp, and he wants Sam to prosecute. But Sam says he needs evidence. He can't prosecute off Jerry's hunch alone. EVERY episode, this dance happens. Well, that's about how customer discovery goes. In this case, I'm Sam Waterson and you're Jerry Orbach. So if you want to learn about customer discovery… let's dance.
There's been a murder, and the detectives show up to the crime scene and look around for evidence. One of the detectives makes a quippy remark, quickly followed by the famous "dunt-dunt" Law and Order sound. Then the detectives take a look at the evidence and start interviewing people who knew the victim. In your case, the victim is the problem, and you need to figure out who has the problem. Your crime scene is your "problem statement," and early interviews help you create a solid "hypothesis."
On Law and Order, they always take a look at the spouse first. They are right sometimes. But they can't be right all the time (or they wouldn't have such a monster TV franchise). Maybe this time it's the mortuary owner or the cable installer or the sister. As you iterate your hypothesis by interviewing people closest to the problem (the victim), you narrow it down to a few suspects to focus on. Then you pick them up for questioning.
One at a time, you put each suspect in the "box." The first thing they do in the interrogation room is get the suspect comfortable. The detectives mirror the facts to date, but they always leave out key facts that have not been in the press. In your case, you talk to the perp (sorry, the subject) about your journey and some key facts that you know. You throw in some names of the other people you plan on interviewing and add some other thoughts. You never put the cuffs on them, nor do you disclose your early hypothesis. You're still framing out your hypothesis. Then you let them go, and tell them to stay in town. Once you've completed all the interviews, you have a set of facts that excludes some people. Like the people who have an alibi or who lack a clear motive (you thought it was the spouse, but there was a prenup). You're now down to your final hypothesis, and you become very passionate about it. You have several facts but no proof.
You go to Sam Waterson (or me), and you say you have all the evidence. You want me to go to the judge for an arrest warrant (the infamous investor pitch deck). In my case you make the pitch, and you close with stating that you want a term sheet. Sam Waterson says, "You have some circumstantial evidence and a hunch, but you don't have proof." Jerry complains, "What do I need to do… have them on camera shooting the victim?" Sam replies, "That would be nice, but a confession would be just as good." Jerry has arrested the perp (trying to sell them) but now has to release them. You tried to sell the person too soon instead of getting solid proof that their problem existed.
Next scene, Jerry has the perp back in the "box." His goal here is to get a confession. "Did you kill the victim?" The perp says no. In your case, you ask "If I can increase your profitability, would you be interested?" and the answer is yes. Both you and Jerry asked a question with a highly predictable answer. Please don't do it.
And here's where the actual customer discovery begins. The goal is to get a confession by asking a series of questions that catches the perp in a lie. In your case, your goal is to ask the right questions so that the person's tone and body language start to give you a better line of questions and indicate where to dig deeper. This is why I always recommend customer discovery be performed in person. There's no silver bullet of questions here. I interrogate with negative questions that create an emotional effect. If I think there's a massive problem with the managing of privacy (see my friends at OneTrust), then I would ask "Don't you think privacy laws are dumb. Such a waste of everyone's time…" In other words, get people emotionally engaged and make them take a position and defend themselves. It works on Law and Order, and it can work for you.