Read this before going into any meeting.
Know your goal
Everything you do should contribute in some way to achieving your goal. What does success look like coming out of the meeting? What would require followups? Your goal does not need to be exactly defined, but you need to at least have a general direction. Sometimes the goal can simply be getting to know someone better - in this case, success could be better understanding of their personality or motivations. Do not get sidetracked by disagreements and emotions; if it doesn't help achieve your goal, move on.
Understand the participants
You know your goal. You know who will be at the meeting (or if not, find out). What are each person's own goals? What are their motivations? Understanding each meeting participant and what to expect from them will help you prepare. If someone is the ultimate decision maker, for example, then you can prepare the best way to convince that person to make a decision that helps you achieve your goal. The dynamics of different people with different agendas can get complicated, so the more you know the better you can navigate.
Volunteer to follow up
Some people consider taking notes and following up to be menial tasks. They are wrong. Think of it as writing history. By volunteering, you get to shape the narrative of what happened and what was important. You can prioritize what you deem important at the top of a summary email for example. Just be careful of straying into historical fiction, or people will lose trust in you! At the same time, learn how to take notes effectively at a meeting. You don't want to be scribbling verbatims while someone is talking to you.
Preview and review this primer for every meeting. Gauge how it went and what you can improve for next time.