I'm writing this for my non-Twitter friends. For those who use it, Twitter is totally obvious, but some people still don't do it.
I use Twitter, not Facebook or LinkedIn. Facebook is friends, family, and game spam. LinkedIn is mid-level recruiters and too generalized.
Twitter is precise - the 140-character limit provides wonderful brevity. Not a time suck like meetings or email.
It's easy to follow multiple interests and industries. For me: YC Alumni, start-ups, Flash/Flex/Adobe, VJs, and media app development.
Who to follow? People & topics you already follow on blogs & forums: heavyweights, locals, groups, and "the source" - i.e. makes your tools.
How to follow? Start with that list and see who they follow. Are their tweets on topic? Are they interesting? Follow 'em. Seed and weed.
Twitter is amazing for news. For example, most Adobe announcements comes through Twitter first (and usually exclusively).
Twitter is also good for publicity. There are apps and plug-ins to automate tweeting your professional activities (blogging, events, pictures).
What should I tweet? Discoveries. Ideas. The occasional rant - it's cathartic and everyone does it. You'll figure it out.
Do I have to say anything? Not really. Twitter is great for passive networking - learning without interrupting or imposing.
Use a desktop app. Leave it running. Look at it whenever. You're not expected to read everything. Important stuff is usually retreated.
[Update] Twitter for OSX was released with the new Mac app store. It's fantastic. Use it.