PM @ Google, before that PM @ Twitter for 2 years. Before that CEO/Founder of a SaaS startup.
Did a BA in Anthropology & English. Learned to write, think clearly, and communicate effectively.
Moved to China, founded a company which failed but gave me the entrepreneurial bug and the realization that I didn't know nearly as much CS as I thought I did.
Went back to school, did a Bachelors of Computer Science w/ Math minor. Learned to think systematically & rigorously, how computers work, a bit of ML/algorithms/etc, and how to code.
Applied to Google APM program. Thought it would be an ideal job before founding a company. Didn't get in.
Founded a company with my best friend, who had a Masters in Computer Engineering and had worked in industry. Spent the first year coding everyday, all our first employees were engineers. Learned to write real software and work with an engineering team.
Transitioned into the CEO role in practice. This happened because my co-founder and I had very different motivations. He wanted to build great systems (and not have to go to meetings / talk to customers). I just wanted to do whatever was needed to move the business forward, I was equally happy coding or talking to investors / taking meetings. Learned (through multiple failings) how to think about markets, interview customers, how to motivate and lead, build realistic roadmaps, raise money, do sales.
After 5 years, sold my company as a 1st base hit exit. I had no problem getting mid-career PM interviews, despite having never been 'officially'a PM. Focused on big scale consumer because I wanted maximize my leverage/impact.
Junior positions? See todd_sherman's response (Hi Todd!).
Skills – well covered elsewhere. The short version is "Get the right things built & shipped." To do that, you need to know (1) what the right things are (user problems, strategy, markets, corporate politics, etc) and (2) get them built & shipped (working with eng & design, leadership, resourcing, more politics). It's harder than it sounds, there are many many more wrong things than right things (and many wrong things can sound pretty right).
I'm sure I'm biased, but I think founding a company is an ideal pre-PM curriculum. When big tech co's acquire companies, the CEOs almost always become PMs, for good reason. This knowledge changes the risk equation as a founder, being a PM at a great company is a pretty awesome backup plan.