Despite what you may hear, there are really only three types of social media "listening" you can do.
There's the operational kind -- you monitor for people talking about your brand or product, and you engage when you need to. This is pretty essential for larger brands now, and is actually pretty operational in nature. You can't sit back and ponder -- if someone trashes your brand and it goes viral, you have can have a crisis within hours. In a more ordinary sense, you might want to try to help people that are just so frustrated they finally tell their Facebook friends or their Twitter followers.
Count and analyze
There's the count and analyze tools. Some are essentially free (you could just search, for example), and some are pretty sophisticated.
If you go down this road, you will want to consider the issue of sampling. This is the challenge of understanding who is doing the social talking, and considering this in your analysis. If you give equal weight to a dozen people who just happened to eat in your restaurant, and one well-known restaurant critic, you may be making a big mistake.
These days, there are tools that will help you gauge sentiment as well -- are the comments largely positive, negative, or something else? When you hear this term, you want to listen carefully. How exactly is this being done?
At it's simplest, counting will tell you what it's predecessor (web analytics) did -- how many people are talking about you, versus your competitors.
This last one is emerging, and the tools to help you do it are still emerging. However, you already possess the best tool for doing this, the human brain.
This approach might help you discover the context for how people use your product or service. (see previous post for more on this.) You might discover that people have trouble opening your bottle lids, for example. Or that people think winter tires are a nuisance. Or that buying a house is a stressful process.
If you have a product connected to important emotional memes, like family, you can probably learn a lot.
I recently completed a study related to the automotive industry, and we did a bit of this last, and found some very very interesting stuff. Of course, people do talk about their cars -- but I was looking for something much more specific, and did find it.
Don't be baffled by the BS
If you are talking to people about social media research or analysis, they are talking about one or more of these main themes. So now you know.