How did you or do you get to know a group of users and their problems?

Be in that user group (i.e. solve your own problems), then see if that applies to others in said group. You could also research the hell out of that group, join the group and learn the business from the ground up, or befriend a person in said group and shoulder surf (watch for dumb issues or ways to streamline the process). My father is in property management, and their entire industry is starting to go online, this is a good example of where I'm able to offer advice.

See http://www.paulgraham.com/organic.html

The best thing you can do is embed, like a journalist in a war zone. Or maybe the better metaphor is an anthropologist, studying humanity by observation and interaction.

Of course, best may not be feasible. So contact and talk to your target group. Find people in it, and ask about pain points. Then make a minimally viable product that addresses one tiny part of it, build a user base, and interate.

Eat your own dog food, as they say. I'm not a developer, but I'm writing a book for a piece of audio equipment I know and love which has an enthusiastic user base but a rather cryptic manual. After yet another day of informal product support on the forums I asked if anyone would be willing to throw down a few bucks for an e-book and the response was overwhelming.

I'm skeptical about stories of parachuting in and solving problems on a short timescale. It's possible but but you need to build your credibility first. I've been using synths and audio FX for ~15 years and only now am I beginning to feel that I have mastery of this particular craft.