Too general a question! Listen folks, every business is different. How it will "fit" into Facebook depends on what type of business it is. How one product or service does it on FB, will not work for another product or service type - necessarily. So it is quite naive to assume that one method will work with every product or service.
However, I believe there is a consensus that FB marketing should be about building likes and community initially than in converting sales directly.
In accomplishing this, there are many ideas for the creative to explore and test. I always say, "look at what makes you look at and then click on a post".
Facebook is all about marketing, for personal or business goals. The important thing is to create the right marketing strategy on Facebook which means that you should be very active there, post different content on your FB page, target your audience through Facebook paid ads, test your ads and then run them. This will help you creating the right strategy for your business on Facebook. Also, you should take a look at some successful pages from your niche and check out how they run the page.
As what the professor said it depends on what type of business we're talking about. If you owned a restaurant, facebook is great to build up as many fans/likes as possible so you can continually market to them your food, specials, new items, etc for example.
Agree with a lot on here, for local business it's key nowadays I would say, easy to reach out to your audience, give them updates of whatever it is you offer. Concering online business, of course it makes sense to showcase your services there. Selling solo ads for example, you'd testimonials (results of your customers) every day. If you're offering coaching, then do some lifestyle-marketing every once in a while, it will push interest when people get to know your awesome life because they want to achieve it, too.
IF you are a service provider.. you can start scouring your current clients friends within facebook. look for the tell tale signs that any of these folks own their own business - or at least have the ability to make decisions. You then ask the current client if they mind if you mention them when speaking to the new prospect. I cal this "facebook referral fishing"
Facebook can be a vary viral tool if it's used correctly (focused on your product or service) and whether you have engaging fans.
But as it was said earlier, one size doesn't fit all so to speak. The method that one person uses may not work for others, but once you figure out what works for you facebook can get your site pages or articles indexed pretty fast.