I have been doing startups for the last 6 years and have had mostly failures, and a single success. I was able to sell the one startup that succeeded for about a year's salary that I would get working at a tech company.
Doing the startup grind all these years has taken it's toll on me and I want to do something that has comparatively less risk for a while.
Freelancing is something that would interest me and give me the much needed mental rest (comparatively) from building startups from scratch.
Without much of a network that I can rely on, how can a "newcomer" go about getting some freelance UI/UX design clients?
Are you sure being a freelancer will give you the rest you need? You will still have to chase every dollar. What about getting a job for a while?
Anyways, while there of course are some sites like freelancer.com etc, I would dig down in my network and extended network, and let everyone know I'm available for freelancing.
Two cheapest ways would be to:
Cold calling sucks, but it's the quickest, most direct way to it. Plus, it's free. Just takes time.
You can also hire someone overseas with minimal or no accent to do outbound calling for as little as $300/month full time. As long as they get you one lead a month it pays for itself and then some. Wouldn't be unrealistic for them to get you one lead a day. Granted, they're unlikely to be high dollar clients, but you can start building your portfolio of regulars.