How to target specific groups on Facebook?

Some suggestions:

1. You can do this with Facebook advertising. You'll be given an option to type in keywords and be shown suggestions of keywords typed by FB users. You can then select them and filter your results further if you wish by options such as age, location, and gender. This at least enables you to target individuals who've expressed an interest of some sort in your keywords.

2. You can approach Fan page owners and offer to pay for a sponsored update. This actually works remarkably well in some niches. The majority of the big fan pages are owned and operated by non-affiliates (in my experience, anyway). Those are the kind you want to approach first, because they generally don't know the value of an update. Just throw a figure at them, $5 bucks say, and see what they say.

3. Join other pages - as your own page - and contribute (don't promote). I wouldn't bother with liking posts, but you can comment and post. Just ensure your fan page name is catchy, encouraging visits when other page members see it.

4. Updates. This is super obvious, but it's worth stating. When you update, ensure that you do so with something niche-specific, and use a call to action at the bottom (in plain sight) to encourage sharing. You'll find only people interested in the subject-matter will share it to their wall.