I found that hanging out in chat was a great way to both soak in, and influence the community culture (actually this is true anywhere, one reason I hang out on SF and AU chats as well. Its also a great way to learn things, especially when they're only tangential to the main topic. Chat turns it up to 11.
I like to snipe crappy answers. My solution to a crappy answer is to try to produce something awesome, with screenshots, in depth steps and such. Its a good way to get rep and improve overall question quality (and not only cause an awesome answer looks awesomer next to a crappy answer).
I often get involved in the tag cleanups when I can't find anything to answer - its a little tricky to do right, and I usually do about 5-6 retags an hour if I don't notice anyone else doing it. Its a VERY useful thing, somewhat underrated, and needs a massive amount of common sense and patience. Remember to pace yourself, since flooding edits is horrible.
Hang out on meta - this is where site policy is hashed out, and once again, you have a chance to get a word in. It also lets you get familiar with the implicit rules of the site, and how things are run.
Comment, especially when flagging, and quote the relevant part of meta or the faq. Except where it comes to spammers, we don't VTC, or flag to punish, we do it to make the site better, and to educate users.
When you hit a new rep level and unlock more abilities to moderate the site, get familiar with them. Notably when you can close questions, you'll find you need to VTC rather than flag. The way a higher reputation user contributes to the sites in terms of janitoring is slightly different since we do more things ourselves and involve mods less.