Get to know the team. Every new team I join, I set up a 30 minute "get to know you" session with each engineer, with only one rule - no talking about work. This helps to build a relationship outside of the work talk.
Get to know the user. Who are they? What are their pain points? Empathy, empathy, empathy!
Get to know the leadership team. What is most important to them right now? Find where value can be immediately added.
Be the Customer (or as close as you can get!)
No such thing as a stupid question.
No technical background, no problem. Building an awesome relationship with my engineers has allowed me to learn an incredible amount from them. I've learned SQL and how to use Splunk on the job. They too like to learn about the business side of things!
Learn how to code (at least the basics). I've taken a few programming courses so that I can be empathetic of my engineers work as well as understand how code is written (so that I can write better requirements).
Relationship Building - My Secret Ingredient
Define the user. Who is the customer? Who is the end user? What are their motivations? What do they care about?
Be the end user. There's no better way to learn the customer's pain points than to literally be the user.
Document Every Pain Point. Document the current pain points (process flow diagrams have helped me here).
Communicate Your Findings. In week 2 of a previous role, I had found a jackpot of user pain points. I communicated these to the executive team and they were completely unaware of these issues.
What's the history of the product? Who built it? Why?
Get to know the product technically speaking. I love sitting down with the engineers for this!
What does the team see as pain points for its product? Again, I love asking engineers this question. They often have awesome knowledge of growth areas, both technical and non-technical.