Set up a Facebook page and/or group where you will post regular news items (from your site and those of other relevant sites). Attract attention to it by posting it in other related Facebook groups (search in Groups for related keywords for your topic). Keep it updated regularly.
Set up a Twitter feed where you will post regular news items (from your site and those of other relevant sites). Attract attention to it by following other similar Twitter accounts (search for related keywords for your topic) and retweet and reply to their tweets. Keep it updated regularly.
Set up a blog where you will post regular blogposts about topical items in your subject area. Attract attention to it by adding other similar blogs to your blogroll (search for related keywords for your topic) and post comments on their blogs. Keep it updated regularly.
If you don't "get" Twitter, there's a remarkably succinct and clear summary of what it is and how it works in today's verdict on the Twitter joke trial. (PDF)
And remember, all publicity is good publicity - except the kind where you are caught trying to sweep your blunders under the carpet. If you do screw up, admit it and apologise. If you have not screwed up, apologise to anyone you may have offended, and point out why you chose to do the thing that you did.