Three ways I'm personally aware of:
1. Respond to public RFPs. Most government contracts are bid this way, as are many private contracts. Be prepared to be undercut by the competition. It's pretty cutthroat.
2. Agencies. I know a number of successful contractors who work through headhunting agencies. Downside is the overhead they add to the contract.
3. Networking networking networking.
In the case of the latter, in the beginning it'll be networking through your peers. Join user groups, industry trade groups, local entrepreneurial meetups, that sort of thing. And make sure you stay in touch with your colleagues... you'll never know when some company they're working for puts a project out for tender.
Once you have a few contracts under your belt, if you're good they'll lead to more thanks to referrals, and that can pretty quickly snowball.
If you go this path the best advice you can probably get isn't what you'd expect: be prepared to say no! The quickest way to fail as a contractor is to take on too much work too quickly. At the beginning folks are usually paranoid and take on anything that comes their way, but trust me, that way lies madness!
Edit: As an aside, it's worth noting there's different types of contracting, and you should decide what, exactly, you want to do. A few examples I can think of:
1. Discrete project contracts. You bid to produce a solution, after which you offer some sort of support or maintenance contract. You probably give up the IP in this case, as it's work-for-hire.
2. Contract positions. You're brought in as labour on a new or existing project. Oftentimes specialized skills are valuable, here, as you're often brought in to fill a gap in the existing skillset, whether that's project management, design or architecture experience, or specific technical skills.
3. Really a variant of the first, and is what I think of as contract-to-product. You bid on an initial contract to build a product, after which you provide follow-up services to expand that product on some regular basis. This could be done by billing out on a line item basis, or via a retainer of some kind. It's possible in some cases to retain rights to the IP for a job like this.
So think carefully about what you want to do. Each model has pros and cons and may effect how you bid, what skills you develop, etc.