In the office's kitchen, making myself a cup of coffee, when the new super-excited Product Manager on his first day on the job, approaches. He is asking for my advise. What should I start with? There is so much to teach a new PM...
Before product development methodologies I I would probably start with the very basic - The way you work with your team and colleagues.
A PM works a lot with a team and the key to success is working working them well.
My first advise session would be focus on these three important elements - Listen, Decide, Improve.
Listen - If you are part of the Product team then you must be a "team player" and that means you work closely with many parties. You are in a relationship, for all that it means... The first rule of any relationship - know how to listen. If you won't listen, you won't be listened to and if you don't listen, you cannot learn and improve.
Decide - Many people CAN make decisions but you are the one that MUST take them. Even when it is difficult, even when it is not trivial, even when it is not comfortable and even when critical things are at stakes. In many cases, you'll notice that many of those people that can decide, sometimes tend to avoid it. You don't have a choice. Train your 'decision' muscle because it is one you will use all the time. With decisions comes responsibility by the way...
Improve - There is no shame in making mistakes, as long as you learn from them. It's an awful thing to fall into the same hole twice...
The one thing that you cannot learn is experience, and that comes with both successes and mistakes. Make sure you turn your bad experiences into a strength.