In my experience (in the UK) you start by submitting your CV to loads of recruiters saying you are looking for contract roles. If they think they can make money from you they'll give you a call and ask for your rate etc.

I'm not the OP, but I just do plain front-end development. Contract length can vary, sometimes it's one week in a digital agency, sometimes it's a few months in a large company. You can also find contracts that are 12months, and they can be extended after that.

I was freelancing when I started out, so I had some income but was also available for full-time contract work during the day.