If you're new to PM, what's a good way to think about, contextualize, and approach a 30/60/90 plan if you've never done one before? Also, are there any templates/resources you'd recommend as a jumping-off point?

The 30/60/90 plan is very helpful for anyone coming into a new role, but specifically for PMs there is a simpler way to break it down. This won't libe up perfectly, but I'd think of it as a product managment process... your first 30 days are for discovery. You are talking to people learning about the company, the customers, the product, the processes, everything. You should be analyzing and synthesizing themes and coming up with hypotheses for what you think is needed, and that will be different at each company. For example, sometimes I've come in and the strategy was sound, the ideas were sound, but the way it was being being communicated to customers and internally didn't make sense. Other times I've come in and the idea itself was suspect. I would approach those challenges differently, but I first need to understand what I am dealing with and then I can figure out how to approach it. That's what your first 30 days are for.

The 30-60 day stage is for concepting. At this point you should have identified some challenges and opportunities and have some ideas or hypotheses on how to have an impact. You will have some ideas that are great, and some that others have tried and failed implementing. It is helpful to uncover which is which quickly. In days 30-60, you should start sharing these opportunities to gauge support and interest from xfunctional groups you will rely on for execution. Pick things that are best positioned for success. For example, don't pick the project everyone is against as your first one. Maybe save that for later when you have more momentum behind you. 

Days 60-90 are for execution. This is where you should start executing on the opportunities you've discovered. Dont forget to promote the changes you are making, but in an authentic way. If no one knows about the things you are working on, did you even do the work? Thats extreme, but you get the point. Make sure people know about the work you are doing and the impact you are having.

One more tip: The biggest mistake I see people make on their 30/60/90 day plans is to do them in secret. At the very beginning of your tenure at the company, you want to align on your plans with your manager. This will be the fastest way to detect whether your expectations are aligned or if there is a disconnect between what you think your should be doing vs what your manager thinks you should be doing. 

In the first 30 days get to know the user you are building for, the problems that they have and how your product or feature solves that. Get to know your team and how they deliver solutions for that problem and what is getting in their way. Ask a lot of questions and take a lot of notes.

Use the next 30 days to get to know your product, you should be able to demo it and do so often. Help out by testing any new functionality, write bugs when you find them and keep asking questions. Get in front of customers when you can to demo or just to listen, what are they saying they like and do not like about the product?

Now you can get in and improve or write new requests. Start small, make sure it solves a real customer problem and that you know how to measure the impact.