Darren Rowse of ProBlogger fame just posted a couple of articles on how he's noticing a welcome upswing in Facebook traffic, a tactic that's working OK for this little site at the moment.
If you've seen my Facebook Page, you'll notice I use a couple of tricks used in the "Static FBML" landing page (see Step 6 in Darren's article).
The Static FBML application supports a subset of the tags full blown Facebook Applications use, but the most useful two work - fb:visible-to-connection and fb:multi-friend-selector
Member Only Content
fb:visible-to-connection allows you to show member (or "liked") only content, which I use to "hide" Step 2 in the Landing Page
You can take advantage of this to offer an ethical bribe, which could be a link to a free report, video etc that's only displayed once user's "Like" the page
Invite Friends
For really keen visitors, the fb:multi-friend-selector shows the common "Invite Friends" Facebook Dialog you see all over Facebook. I can't track how well this works, I suspect it's very low on a landing page, but you could easily create a second page and host this, and then try to encourage existing members to use it if they're liking your content.
Free Code - Facebook Landing Page
You can see the basic outline of my Landing Page in the code below. Just follow Darren's steps to setup your page, then paste the FBML below into the Static FBML dialog and you'll see it working. You'll want to customise the HTML around the FBML tags with some pretty images/your own text, it's pretty straight forward -
Download (Right Click, Save Target)