Not a week goes by in which someone doesn't ask me where to look for freelance work. I've been able to make a living as a freelancer for 10 years now, so I have some insight into how to find gigs.
One of the best places to look for freelance work is a job board. There are several out there, but my top three favorites are:
There are other boards out there, but these are my go-to place for looking for jobs. I haven't had to apply for a freelance gig in years, but I occasionally cruise the boards to see if there is anything interesting.
You can look for freelance work other ways as well. You might be surprised at the opportunities that can come when you are active on social media. I've lost count of the clients who have found me through Twitter and LinkedIn. Share your good work on social media, and someone is bound to notice, especially if you take the time to cultivate relationships online. I may not love social media, but I can't deny that it's helped my freelance career.
Finally, another good way to look for freelance work is to just do a good job. Over time, your reputation will grow. It takes years, but after a while, you will be recognized, and clients will start coming to you.