Different parts of the W3C do things differently. The key Working Groups (HTML, WebApps, CSS, SVG) tend to follow whatever the major browsers' implementers agree on, so no one other than implementers can really cause much trouble. Of course, sometimes implementers won't agree on something, like media format support for <video>. But there's not much to do about that. Fortunately, right now all the major browser implementers are largely committed to interoperability, so we don't have a lot of obstructionism.
The active participants in the Working Groups I'm involved in tend to almost all be employed by one of the major browser implementers: Microsoft, Mozilla, Google, Apple, and Opera. Some of these (Mozilla, WebKit, Chromium) are FOSS. There are a nontrivial number of people participating in their spare time, too. I was one for a few years before I started getting paid to do it this year.
The groups I'm active in (HTML and WebApps) don't do anything significant by phone or in-person meetings. It's all mailing lists, IRC, and bug trackers. They're really run like open-source projects.