Yeah, getting promoted from within is the easiest route. If you are employed now, try talking to your manager and seeing if there are any opportunities. If it's a small team, you may find that you can transition pretty easily just by volunteering to do all the grunt work for planning and writing up acceptance criteria and talking with stake holders, etc.
If you already have project managers in your company, I would get friendly with one or two and tell them that you are interested in learning how to do the job. If you work with one in particular on your team, then ask them if you can sit in on stake holder meetings (with your manager's approval of course!), etc.
If that avenue is impossible, then I would try to find a recruiter you can trust and say that you are looking for a job where you can transition to that kind of role. Recruiters are often looking for that kind of person. Experienced project managers are often quite expensive. It can be a bit of a gamble when you are hiring them because the job is quite difficult and skill levels are pretty variable. If you can imagine the impact of a developer that has a bad attitude, now imagine the impact of a project manager with a bad attitude :-) One of the cool things about the role is that you can have a kind of multiplier effect -- but that effect can be fairly destructive if there is a problem.
Anyway, I've definitely worked in groups where we were begging recruiters to find someone who could start as a developer and then transition into a project manager... Never even got a single person to interview :-).
As far as training is concerned, it's probably not going to be possible. In the ideal world, organisations would know what they needed and be able to train up people to fulfil that role. In the case of project managers, usually they just wing it :-) (As a sidebar, the absolute best project managers I've worked with were either trained as building architects, or worked their way up from being a personal assistant -- so you can get an idea of the kinds of skills you need).
Again, if you don't feel confident in doing the role right away, I would inflict yourself on your current team and experiment :-) There is just so much work to be done all the time on gathering requirements, understanding acceptance criteria (and documenting it), writing up notes for the "big picture", making charts to help people understand progress, communicating with stake holders (even if it's just walking up to them and being friendly, so that there is as to build up a good rapport), etc. If I was on a team that didn't welcome some help in that department, I would start looking for another situation anyway. As is often the case, you may have to put in a few hours of overtime here and there so that you have time for the extra work, but eventually people will start to depend on you and you can easily justify it in your normal day job.