First, find a PM to talk to, especially one you admire who's made the switch. Everybody's situation is different, and having someone to mentor you through it is invaluable.
Second, make sure you have the right motivations. A friend of mine says "run to product management, not from engineering." If you want to switch because your current manager is a jerk, you hate the project you're working on, or (gasp!) your PM is an idiot, you might be doing it for the wrong reasons.
You could test it out with a small project at first. Stepping up and saying "I'd love to take on more of a PM role on this feature/bug/release" will often be positively received by a healthy organization.
Startups are ideal places to make the switch (that's where I did it.) Everyone is used to wearing many hats and the "all hands on deck" attitude is much more welcoming of someone raising their hand and volunteering to be a PM. Smart, bigger companies (like Google or Facebook) often have formal programs for moving into PM. At Google, for example, we even have a six-month rotation program that lets you try it on for size.
And if you're convinced you want to do it and your current company discourages you, find a new one.