What are some of the best ways to begin becoming a more influential PMM?

Influence comes from repeatedly bringing fresh insights and a distinct point of view to the table. To influence product strategy and the roadmap you need to take a broader view of your market and the customers than your friends on the product management team. Invest in a deep understanding of your customers, your competitors, and the market at large. Map out mid- to long-term threats and opportunities. Validate those threats and opportunities with customers, industry experts, and your internal experts across product, user experience, customer experience, sales, sales engineering, and client services. Summarize the insights, provide the market context, and lay out strategic options together with your product partners. Get buy-in from the executive team. Partner with the product team to deliver solutions that solve real customer problems. Rinse and repeat :-)

• Demonstrate the basics: messaging, positioning, ability to make an impactful/relevant/meaningful presentation that conveys the value prop + differentiators of your product or portfolio. Cant be influential if your house is on fire. 
• Learn the business REALLY well. How is money made, who do we sell to, how is the sales team structured, what are their main sales motions, is it self-serve/direct/partner driven? Learn it ALL. Then figure out where are opporutnities to add unique value: better targeting, better messaging, more customer interaction, roadmap changes. Dont try to change things you don't understand
• Do what you say, fast. Dont make excuses, just get it done. Then your credibility will go up.  
• Have a POV. Why are things the way they are? Test out your POV with sales, product, CSM, other stakeholders and refine it. But have a POV, and when the time is right, you will get your shot to make that POV into reality

Product marketers have to work and communicate with a wide variety of stakeholders to push ideas and initiatives forward. Influence is critical for PMMs to be effective, and that comes with building trust.

Invest time in understanding your stakeholders’ needs and pain points to help you determine how you can best work with them. By speaking the same language as your stakeholders and proactively providing the insights and information they need, the more they will lean on you and trust you to get the job done.

Immerse yourself in your product, the market and your customers. Use those insights to identify opportunities where you can add value: influencing product roadmap, helping your sales team close more deals, ensuring your messaging is compelling, etc. Bringing valuable insights and a unique point of view to your stakeholders will improve your credibility and make you a more influential PMM.

I read the other answers, and there's some good advice there. However, there isn't much "how" in the answers. Have a point of view. Demonstrate the basics. Communicate across teams. All great advice, but how do you demonstrate that, preferably quickly?

It's simple.

Blog.

Blog publicly. Blog internally. Just write. Write your point of view. Write competitive insight. Write what your audience (mostly sales, but also execs) needs to hear. Some won't listen. But more importantly some will.

I'm a founding PMM at a small company, so my CEO was all over our public blog (which was dead until I joined).

For sales, we don't have a blog, so I wrote in Confluence and shared in Slack.

The tools don't really matter. In other larger companies I've created a pseudo-mailing list cobbling together internal tools, that was really well received (by sales and my peers in product).

Writing clarifies thought... so it helps accomplish what other answers to this question suggest as well. How do you develop a well articulated point of view? Write! How do you create compelling differentiation statements? Write!