Be honest, and ask for a story (and be prepared that a lot of developers are bad storytellers.)
Before doing anything, learn. Even though you are not a techie, you still have to know what your are talking/asking about. If this is a library that helps interacting with a service or some special hardware, make sure you know something about that service or hardware. If itʼs a support library, make sure you know, on a basic scale, what the library is capable of. If itʼs a UI component or a whole application with a UI (be it web or desktop), get to know what it looks like and what it can do. Also, if you have competitors (and who doesnʼt these days), get some basic knowledge on them, too. At this point you are authentic. You will still learn a lot during your career, but without basic knowledge you are screwed.
Meanwhile, you can start gathering information on people using that software. Collect names and email addresses, and stalk those people (stalk is a harsh word; I mean do intense research on said people.) The main point is to know them and what they use your software for before you ask.
Now you have the knowledge and the data, approach your favourite developers in house. This serves two purposes: you get some exercise, and gather more inside information of your software. Find the guys who not just develop but also use that software. If thereʼs good diversity among the devs (gender, different cultures, etc.) try to find as many different people as possible. Ask them the questions you would like to ask from the actual audience.
And now, contact the consumers of your software. Ask for their story. How did they find your stuff? Why did they choose it over other, similar projects? Are they using it for its intended purpose, or something else? How do they use it? Is it part of their daily job, or something personal? Are there any pain points, bugs, or missing features? What are their favourite parts? If they could choose, what would they make the devs work on? If they wouldnʼt have to care about backwards compatibility, even within their own software, what feature would they remove or change and why? And a lot more.
Most importantly, keep in mind you are stealing their time. Be as short as you can. If they donʼt have the time to answer, ask for a time slot (if you talked with other devs before, you will be able to tell how long it will take.) Donʼt ask irrelevant questions; if you already know an answer, phrase the question like “am I right that you use feature X the most?”. Also, what you are interested in the most are feelings, especially if there is UI involved. If you can meet in person do it, so you can read their emotions. Or maybe donʼt, at least not until you have some answers and experience already.
I think thatʼs all. Iʼm sorry if I wrote something obvious, but without knowing the details both about you or the software, I tried to be as generic as possible. Feel free to ask more in the comments, Iʼm happy to update my answer with more details if needed.