I see two challenges here. The first is to get people in the door for the first time. Referencing the site in blog posts, tweeting out interesting questions, SEO and generally mentioning this site to anyone tangentially involved in the Tridion world will all help us get people in the door for the first time.
The second challenge is to get people to keep coming back. While all the same things that got users here the first time will also lead them back to the site in the future, the experience they received the first time they visited the site is also going to be a big factor in whether they become a recurring user or not. During their first visit did they find information that helped resolve their problem? If so they’ll likely be back, if not they probably won’t be back.
So what are some specific things we can do on the Tridion SE site?
Write good question titles - When you post questions try to write good titles for the questions. Typically when a Tridion SE question shows up in a Google search, the result title comes from the question title so a good title is more likely to let the user decide if the result is worth clicking on or not:

And when a Tridion SE question shows up in a Bing search, for some reason the only portion of the question that shows up in the result is the first part of the question title which makes good question titles even more important on Bing:

Notice how Bing is showing the same abstract text for all questions Tridion Stack Exchange is a question and answer site for Tridion developers and administrators. It's 100% free, no registration required.
This is different than what I see for other SE sites (and even questions from our own Meta site) but it just means it is even more important to have good question titles.
Use good, relevant tags - I’ve actually been wondering if some of our abbreviated tags might be a bad thing from an SEO perspective. Are users going to search for ‘dwt’ or ‘dream weaver templating’?
Spelling and Grammar - Use proper Spelling and, to the extent it affects people’s ability to understand the question or answer you are posting, proper grammar.
If something doesn't look quite right, edit it - If you see a question/answer that could be improved, whether it is rewriting the question title; fixing grammar issues; fixing formatting or ensuring code snippets follow best practices, don’t be shy: Jump in and edit the question/answer. Right now only a small portion of our community is jumping in and editing posts on a regular basis.
And how can the Tridion Bloggers help get more people in the door?
Reference Tridion SE questions in your blow posts - When you are writing your blog posts conduct a quick search on the Tridion SE site to see if there are any questions you can use for reference purposes in your blog post list Nickoli Roussakova did in his post Fixing Tridion Content Delivery Deployment Errors: “Unable to load DLL ‘xmogrt’” and “System.BadImageFormatException”
Mine this site for blog post topics - The Tridion SE site could easily be mined as a source of topics to cover in more detail in blog posts. For example, to me the question Multiple Publications - One broker database just cries out for an expanded blog post covering how to make the decision of 1 vs. many broker databases for different Tridion usages scenarios. So if you see something that piques your interest write a blog post about it and make sure to link your post back to the question here on the Tridion SE site.