What is a good way to make the transition from software engineer to product manager or from software engineer to account manager?

Product management, and account management are as you suspect very different roles. A product manager, what people usually mean when they say PM, defines what the product or more commonly in big companies, what the new features of an existing product will be. In addition to how you see PMs interacting with Engineering, they also have to work up the management chain to get executive buy in (unless the idea came from the top), laterally to get cross functional support, with marketing to get the appropriate exposure, and with sales to get customer feedback. PM roles at top companies generally desire an MBA. An account manager works very closely with high value customers to ensure they stay on with the company and increase their spending when appropriate. A technical account manager is expected to be able to answer some amount of technical questions without having to come to the engineers. An account manager role is more of a sales role. If either of these roles are what you want to do, there is no benefit in waiting or transitioning slowly. The skills you develop as a senior engineer won't get you slotted in as a senior PM or AM. There is some experience you gain as a developer in product life cycles, but if you really want to change career tracks, you have to just do it. The sooner the better.  But as for your question of how to do it, You can get an MBA and use your MBA internship to get a PM role. You can work for a big company that has a formal job ladder transfer program. If there is no formal program, talk to your manager about how you can get the experience you need. Or, you can join a startup as a dev, but also do PM or AM work. However, as a first step, I'd suggest browsing through some job listings on linked in so that you can clarify what you want to do. Then you can make a clear transition plan.

I've written a lot about how to transition into product manager. This post summarizes most of it: http://www.producttalk.org/2012/09/so-you-want-to-be-a-product-manager/ You might also be interested in an interview who successfully made the switch from engineering to product management: http://www.producttalk.org/2012/08/moving-from-engineering-to-product-management-with-zaz-harris/ The key premise in the series is that you have to show that you can do the work. That means  you need to: understand what skills and work is required to be a product manager work on developing those skills and your ability to do that type of work find a side project or a project at work that allows you to showcase those new skills and abilities.

I agree with the other answer. As an engineer/developer, you don't need any more experience in you field. Not sure why you would want to unless you prefer people interaction to computers.

The main skills you want to gain as a software engineer if your career ambition is to migrate into product management are: Talking the talk Understanding how engineers communicate, and being able to translate that when you write PRDs, user stories, deliver presentations, and the like is a very advantageous skill to have. You'll more than likely be pushed into more technical product roles because of your background, and so pay attention to this. Understanding how products are successfully built by watching how good product managers work (and conversely how poor product managers fail) Watch what it is about successful products. Was it the research? Was it the marketing? Was it the SE who built the demo? At the same time though, focus on what about the engineering team allowed it to succeed, and make sure you look for projects with similar teams. Area expertise Become an expert at a product. Understand its customer. Know the market. This is the one piece where being the engineer may be a disadvantage, but you have to turn it into an advantage. All in all though, this is a 2 - 5 year journey at a maximum. Otherwise, I think you'll find yourself too senior in one role to transition to the new one.

http://www.startupinstitute.com/ is probably the best educational program for career transitioners.