Welcome to the world of social media.
Sound like you've been tasked to drive metrics before being given a chance to figure out a strategy. And that's a problem.
What do I mean? Well, Facebook is great for many things but someone clicking to your site? If you have a coupon, sure. That's not really social though... but it will get you traffic from a social site. On the other hand LIKEs, I can show you sites where you can buy fans... big numbers, not big cost, but uh, what are they going to do for your business not even knowing who you are? Now when you talk about the impact of having a dozen customers share a positive comment on your product, that tends to mean big results, but measuring it is not so simple.
Before you start deploying you absolutely have to figure out what engagement means for you and for your company. Anyone can make a fan page and start talking but if you don't know why you're doing it, or what people are going to say, you may wake up to a not so fun morning. Social isn't about having a check in or a page on a given network, it's about getting involved in a conversation that's already happening, growing it, and using that all to show the world what your brand offers -- not just from your own voice.
So that's the big statement but as far as what you can do, well, it really depends on your business, resources and market method. A foursquare checkin promo isn't exactly social [it's a coupon] but it can work well for a chain of stores, not so much for a virtual based company selling virtual services. Facebook is a little more straight forward as people will be coming for service and questions [if you have customers] but unless you want your social channel to be nothing but support [not good], you'll have to find a way to go beyond that. And of course while Facebook is the biggest, it's not always what people use in respect to your business [Cat does a lot on social but Facebook is just one slice of their network for a reason].
While I realize that doesn't answer much specifically, you're asking the right questions to find success rather than just going to a social site with a traditional marketing tactic as so many do. If you can explain more about your business, I'd be glad to get more detailed.
Take this however you want of course
You can find many great blogs on social campaigns but be careful, there's a lot of fluff too. I suggest following Jay Baer, The Altimiter Group, Unmarketing to name a few.