People are coming to product management from all sorts of roles, sales and marketing not being the exceptions. Coming from strictly business roles such as marketing or sales, people usually bring their unique perspectives into the new role.
Sales folks are known for being master communicators, they're comfortable with talking to customers to understand their problems and find solutions that work for them and for the business. That market knowledge and communication abilities make their transition to a product role smoother.
Marketers are experts when it comes to customers. They know who the customers are, what do they want and how the product should look to satisfy those customers. Marketers look at the entire market which helps massively to create pervasive products.
Leverage your strengthsBecoming a PM might be quite a challenge for a salesperson. Suddenly it's not about the next big deal, not about closing and even not about satisfying one huge customer. However, sales folks are superbly adaptable and could leverage their customer knowledge and communication skills to start a successful PM career.
Marketers should also start by bringing to the product table their expert knowledge of the market. They could provide a ton of value right away by helping the wider product team to understand customers' problems better and bounce their ideas about a product that could satisfy customers' needs.
For both sales and marketing people, product discovery should come pretty naturally so it is the logical place to start their PM careers while they're setting themselves up to speed on the other parts of the role.
Another big advantage for both - their communication skills. Any PM role relies on the individual's ability to galvanise support and lead people without formal authority. For PMs, it is crucial to have strong working relationships with both sales and marketing. So if you come from those backgrounds as a PM - it would be much easier for you to get support.
What to learnMainly - delivery. Odds are neither sales nor marketing people dealt directly with engineers before. And if they did - it might have been challenging. The tough relationships between those functions and engineering are notorious. So sales and marketing folks should not be massively surprised if they are met with degrees of hostility by the engineering teams when they become fresh PMs. One way of handling that would be to distance yourself from the "how" of a product until you learn your ropes as a PM.
It's fine to admit your limitations. It's even better to find an ally in a dev lead who can lead the "how" part while you're providing the "why" and "what". However, to become a well-rounded PM you'd have to learn the delivery part eventually. Being technical as a PM helps massively even if it's not a must-have requirement.
Another thing mainly for salespeople to learn is the pervasiveness of a problem. Naturally in sales, you'd focus on one customer, maybe on a few, and their problems. As a PM you'd need to check if those problems experienced by a larger group of customers - the more the better. Some marketers, who specialise in particular market segments, might also benefit from learning problem validation techniques as part of product discovery work.
How to test driveFor marketers it's much easier to have a taste of PM work - marketing is usually a part of a wider product team. They tend to take part in the discovery, product definition, go-to-market and growth stages. That's a lot of exposure and will give marketers a good idea about PM job and whether they want it.
Additionally, marketers might take on projects such as creating a landing page or re-designing the marketing website and run it as a PM would. That might be the perfect opportunity to be a PM without committing to a job title change.
For sales folks, things are a bit trickier. Usually, sales are under huge pressure to close deals, it's a high-intensity role that leaves very little to no free time to try something new. However, there is something you can do in sales to work closely with PMs and observe if that's the role you might want. Your best bet - customer interviews. Bring your PM on a call with you, any good PM will jump on a chance like that. Listen to how they talk to prospects or customers, what questions do they ask and then follow up to learn what PMs did with this information.
Another way is to team up with PMs and marketers in go-to-market activities. There you'd be able to learn how the product was discovered, what problems it aims to solve, how it was scoped and what qualities future customers will find the most attractive. In essence, you'd want to make some PM friends and help each other with your work goals and aspirations.