How do you, as a contractor, find this sort of work?
So: email everyone you know (also non-programmers) a 4-sentence email that you're now a contractor. Explicitly list the domains and technologies you can "hit the ground running" at, and focus on those. People need to be able to see you as "a great Java programmer" or "a great iOS programmer". People have a hard time wrapping their minds around "a great generalist" so don't make that pitch.
Set a high rate from the start. Ask around what's common in your area and go a bit above average - some of your peers are likely charging to little. You'll find that customers don't typically negotiate rates - instead they'll just assume that this must be what a proper contractor costs. You might miss a customer that way, but that's the customer you don't want, the kind of customer that will make you regret contracting. Time-sensitive customers are ok (after all, that's what you sell right? hitting the ground running?). Avoid price-sensitive customers, they're hell.
Sell by the day or week. Not by the project, cause projects always blow up and you don't want to take that risk.
That's it, really.
Would you then use a recruiter or something like that? I don’t think I would get any gigs using my network.
One thing you might find is getting your first contract is hard if you are in a permanent job - companies generally are looking for contractors to start ASAP, so a one month notice period (with the risk that you get tempted to stay at your existing company) is often not acceptable to them. Some clients will wait for the right person but you might find you need to quit your job first before finding work which can be a bit nerve wracking - so it’s wise to survey the market, talk to recruiters etc. for a while before doing so!
If you’re UK based https://github.com/tadast/switching-to-contracting-uk/blob/m... may be interesting.
One way is to try and get some sort of security cleared job. Once you do, you immediately elevate yourself away "from the crowd" of developers in the market and you will find major global companies want you and they pay well. And when you get your first gig, you can be sure that another company will want a security cleared engineer, so it's good for job security.
Just be careful how you say no when they ask you if you want to join on a perm basis :)
you become an "employee under guise" and then you will be taxed as such. then you get the worst of both worlds.