If you care, or for others who haven't yet approached Stack Exchange sites [1] in the wrong way and found themselves put off as a result, the way to start building reputation is by
answering questions, not just accurately but as extensively and generally as you can manage, with bonus points for considering edge and corner cases. Play to your strengths in terms of domain knowledge, especially in relatively obscure domains of which you have extensive knowledge, and don't get discouraged if you are not immediately lauded; SE pages tend to rank very highly in Google searches for topics to which they have relevance, which means that if your answers are sufficiently valuable, they will be found and upvoted over time; in terms of reputation, which SE makes the essential currency of being able to do things such as edit questions and answers directly, this 'long tail' effect is considerably more valuable in the long term than getting your answers accepted. (That green check mark is worth 25 reputation points, once per answer; each upvote is worth ten, as often as someone with an account finds your answer of use. Answering the specific question in a quick and narrow fashion is more likely to get you the check mark; answering extensively and in detail, as I describe here, will certainly get you upvotes over time, unless no one but you and the asker cares about the subject anyway. Which buys you more rep? You do the math.)
Is it necessarily worth playing the Stack Exchange game? Certainly not, especially as the sites have grown to an extent which strains the moderators' ability to manage them -- Super User, I'm looking at you in particular, and the flood of undifferentiated garbage questions which has increasingly occupied your front page since I created my account a year ago, and Stack Overflow, you're hardly better, thanks to the endless zombie hordes of idiot PHP hacks who ask the same stupid question twenty times rather than try a single Google search which would certainly turn up the obvious, simple answer. Worse, in fact, as the original developer admits [2], the Stack Exchange model is explicitly designed to be addictive, and he and Spolsky nailed it; if you're not in favor of time sinks, Stack Exchange is probably not for you. But if you're a domain expert who finds interesting questions appealing, or even better someone who finds that the best way of gaining knowledge of a given domain is to work out how to answer other people's questions about it, you might do well to try out a Stack Exchange site.
[1] Except for English Language and Usage, than which you will never find a more wretched hive of snark and pedantry; unless you're a tenured professor of pointless linguistics, your time will be better spent on almost any other activity, be it Wikipedia editing or toenail bonsai.
[2] http://www.codinghorror.com/blog/2011/10/the-gamification.ht...