In my opinion, the best way to learn something about your product is to use it. Not in an artificial testing situation or powerpoint presentation, but really use it.
Walk a mile in your user's shoes. Literally. Go where they work, and do their work for a day using your product. If you need to explain why you are there to external customers (so the people that are serviced by your customers with the help of your product) you can always just say you are new or an intern.
Not only will you better understand your users and product, you might come up with idea how to improve your product that your user's could not think about or formulate properly because they don't know what options exist.
(As an example that I always use in those situations, I always thought the interface design of one of our apps was really badly thought out and implemented by a sloppy 5th grader, because it broke every single standard of color and size. Until I actually worked in the warehouse where they wore clumsy, protective gloves in shady lighting conditions and orange lights blinking in the background and instead of pulling of the gloves every time they used the computer, they just kept them on and needed a less sophisticated interface because it's hard to hit a normal button with the mouse when you have protective gloves on. From that point on, that user interface was pure genius in my eyes because it really worked for that situation.)