The thing I think a lot of people misunderstand about promoting something locally is that there really isn't an art to it. Yes, you can be creative, but when I think in terms of spreading the word, I think of it as more of a procedure.
The first thing you have to do is look around you. What resources are at your disposal? What time do you have available? Do you know anyone who would be interested in helping? How much money can you afford to spend on it? Are there any existing materials you can use and expand on?
Since this is intended to be a primer, we'll focus on the most basic things you can do. Surprisingly enough, the time and money invested in such a campaign is next to nothing, but if you want to maximize your efforts, you'll need to recruit some volunteers. We'll get to that in a bit.
What are some of the ways I can promote the site in my area?
The least expensive, easiest, most basic thing you can do to promote the site? Talk about it. I've talked to a number of people about the site, either in an uncontrolled spasm of joy at a website you're known at, or in person in normal conversation. I once casually mentioned the podcast to a friend on the phone, and he had not only heard of, but had visited and carried a favorable impression of the site.
A word-of-mouth campaign is possibly the most powerful tool at our disposal, but it takes you to help it along. This is how websites get popular. It's how businesses get patrons. It's how phenomenons such as lolcats or rickrolling spread. You don't have to spell out "thinkatheist.com" in fireworks on the 4th of July to get attention. A trusted referral goes a long way.
There's one thing to keep in mind about promoting on other websites. If you're new there or people don't know you that well, it's likely that you'll cause more harm to T|A than good, because people will think you're a troll or a spammer. I recruited chiz by posting a blurb on another website's IRC channel, and he turned out to be quite an active member.
Okay, that's easy enough, but I can't talk to everybody I bump into.
Nor should you! Let's take a moment to see what other resources are available to us. The easiest thing you could do at this point is print out some thinkatheist.com business cards, which can be found here: http://www.thinkatheist.com/forum/topics/think-atheist-biz-cards-pd...
You can give these out to friends, pass them along at campus gatherings or atheist/secular conventions or any other social gathering where there's an opportunity to schmooze. Put them up on public bulletin boards where people post help-wanted ads. You can get creative with it, too. Instead of business cards, how about printing them off and cutting them as stickers?
Don't like the designs? Come up with your own, or post a request for a new design. This could include cards, fliers, or stickers. Don't be shy! If you want it, it couldn't hurt to ask.
Later I'll be talking about how to go about promoting on college campuses and connecting with other atheist groups. If someone has ideas about how to form a secular group, feel free to post a tutorial.
For those out there who are willing to invest a little bit more time and money into promoting atheism and plugging the T|A community in the process, check back for updates!