This is a very important topic. Let me note that some queries already place cs.SE content reasonably high, for instance "prove language not context-free" (duckduckgo, Google) and "why is quicksort fast" (duckduckgo). I assume the situation is similar (and improving) for other popular questions.
Another observation is that when we had a huge spike of visits due to a tweet and/or reddit, some of them stuck. Ever since that peek, our average number of visits has been higher (from around 300 to around 350). That suggests that we have something to offer and people come again once they know of us at all.
In general terms, we want
- people to come here with their questions and
- people to find our answers.
The two items are strongly intertwined: better questions mean better answers mean more exposure mean more people with questions. In order to achieve these, we have to
- be known and respected among computer scientists (of all kinds) and people using computer science and
- be searchable.
Again, these issues are not independent.
In order to be known, we have be visible for our target group. Search queries may be able to do that to some extent in the future, but right now we rely on word of mouth. We have to literally spread the word when talking with colleagues and friends, posting content on the web and attending meetings. Some people will do that casually because they had a good experience, others will put in honest effort because they care about the site as a whole.
In order to be searchable, we have to be linked (by important sites), plain and simple. Other than waiting for satisfied users to link to us, what can we as core community do? I think we can mainly inject links to our good content in other communities, for instance other Stack Exchange site, Wikipedia, newsgroups, social networks, etc. Other than that, we have to work on the first item and rely on the powers of the crowd: if it is good, they will link it.
One issue I personally have with advertising is a lack of brand. We have no logo, no pitch phrase, no nothing. I am considering to initiate an effort to develop prototypical elements we can put on (website) banners, posters, powerpoint slides, shirts, stickers, you name it. I think I could motivate more than one professor to plug our site, but for that we need a memorable presentation. What do you think about that?
One issue I have no solution for is language. I would expect native speakers of other major languages (Spanish, French, Mandarin, even German) -- especially pupils and undergrads, maybe also practitoners -- to search in their own language. They won't find us this way. So we have to put extra effort into advertisement to non-English folks. Maybe blog articles in several languages pointing here can help?
Furthermore, note that most of our questions fall into TCS. This is probably natural as students tend to struggle most in TCS, and we have more experts in TCS than in other subfields. However, relatively few people are deeply interested in theory so it stands to reason that we can expand our audience considerably by widening our practiced scope (in defined scope does include all CS).