This might seem counterintuitive, but the best way to start booking paid work is to complete a little bit of free work to build your portfolio beforehand. People are (understandably) reluctant to pay someone who is "just starting out" unless they're looking for a bargain, which is a whole other topic worth discussing later. For now, we'll just stick to the market you should be targeting: people looking for quality photos.
The key is almost too simple; just take a lot of photos and post your best work. If you're a college student, it won't be hard to find at least a few people who would be thrilled to get a new Facebook profile photo for free, or a young couple who would love to take an afternoon and let you photograph them. The way you'll stand out in the market is precisely because you'll be showing your work instead of just asking people to pay you for your mystery product. The college campus market is already oversaturated with people trying to make extra money taking photos; be the guy or girl who's putting up photos on your timeline instead of advertisements. My buddies Matt Owen and Greg Knopp are great examples of this. They're posting all the time, and to be honest I never know what's paid work and what's for fun; it's just all good work that they're consistently presenting.
Why free work is good for your business (at first)
It displays what you do
I can confidently say from experience that the most valuable step I've taken in my photography career has been to just take a ridiculous amount of photos (before and after I started getting paid for it). Free work is the spark that starts the wildfire. It's what shows people you're more than just another kid with a camera and a kit lens.
You get better
Unpaid portfolio-building is more than just a metaphorical display case for your talent. It's also a great way for someone with not a lot of experience to work on his craft, to get to know his camera, to be able to focus solely on the creative aspect rather than on whether you're using the right settings. Read this next sentence carefully. Everyone's work sucks at first. There are very few exceptions to this rule, and I'm not really sure I know of anyone who is. Most of the photographers in my circle look at their old work and want to punch themselves in the face, which is good; it means they've grown.
It gets you exposure
This sounds similar to the first point, but I mean it a little differently. I'm not simply talking about people becoming familiar with your work; I'm talking about people becoming familiar with you. As you continue to share work, your style and voice will inevitably show up. People will begin to see consistency in your work, which will attract some and deter others, which is really fine. Finding a niche in the market is a great way to avoid working for clients who hired you because you're a bargain rather than your style.
You gain confidence
Being confident with your own work is a process, and it isn't a short one. But having a base of work that you can show paying clients when they're thinking about booking changes the conversation from "please trust me" to "here's why you can trust me." That will absolutely have an effect on the way you communicate with potential clients. Having an established style and voice in your art not only shows your audience what you're going to present to them, but it allows you to confidently produce work without compromising your style simply because you don't know if they'll like it. If someone sees your work and decides to book you, there's no "I really hope they like this" moment.
I understand that free work doesn't pay the bills and that there needs to be a balance between the time you're spending doing free work and time spent making money. It isn't easy, and your photographs won't bring in a ton of money right off the bat. Do yourself a favor and don't stress about that. Understand that having a day job and being a Creative is a totally acceptable stepping stone. I worked as a door-to-door salesman for three months just to buy the first bit of gear I wanted to shoot weddings with. Set aside your pride, do what needs to be done, and set yourself up for success.