Hi Chris,
Picking up freelance work will be more difficult (but certainly not impossible!) if you're a student without a lot of professional experience. Most of the freelancing websites are a bloodbath race to the bottom where everyone wants work done as cheaply as possible. Toptal is a bit different, as the barrier to entry is a lot higher, so you might find it more useful than sites like Freelancer and Upwork.
You might also find the freelancer "Who's Hiring" posts here on HN useful. They pop up on the first day of every month, and you can find them archived at http://hnhiring.me/. Posting that you're available on there could be a good way to pick up some work.
Having a good portfolio page of work you've done can help tremendously. I've always liked Michael Fogleman's projects page: https://www.michaelfogleman.com/projects/
To stand out from the crowd, you don't need nearly as many projects as he has. 3-5 would probably be enough. They don't have to be huge! I've always liked downloading the GTFS schedules for a local transit agency and creating a site that makes it easy to look up schedules and stop times. It usually isn't difficult to make one that looks better and is easier to use than the actual transit agency site!
You could also do something interesting and unusual like implementing a cat detector using OpenCV and Python: http://www.pyimagesearch.com/2016/06/20/detecting-cats-in-im...
If you learned how to do that from the blog post, reimplemented it yourself, and then put some of your own customizations in it, you'd have something good to add to your projects page. Someone who had a project like that they could show me and talk about would stand out (in a good way) from 100% of the developers I've interviewed in my career. So maybe try getting a few projects up and then post on the next HN 'Who's hiring freelancers' post. There are no guarantees, but plenty of people have found good freelance gigs that way.
If there are any local developer meetups, those can be a great source of work, too. My first ever paid programming work happened because I went to a meetup and showed off a transit app I had created. I didn't have any professional experience at the time, but showing that I could actually execute and ship something convinced them to give me a chance. So having a projects page can help you here too. Other devs that go to meetup often work for companies that sometimes have extra work they need done. If they meet you and like you, and can see that you're able to take on projects and complete them, you'll be at the top of the list of people they'll contact to do work for them.
Hopefully that is helpful!