A 3 step plan
Step 1 - Get some experience with long term contracts with large companies
My experience in the UK is that if you have a high level of skills in a mainstream technology (Java, C#, PHP etc) then there are long term contracts to be had across the country with medium to large enterprises.
Typically, these are available through agents who are on the preferred supplier lists for these companies. You provide software development services for the client (the large company), they pay the agent, the agent pays you.
To get an agent to notice you, simply post your CV on to one of the main job hosting sites (WorkThing, Monster, JobSearch etc) and make sure you have a good LinkedIn profile.
Step 2 - Once in, network!
Once you're in the company network like crazy - especially with other contractors. You are looking to build up a long list of excellent developers that you are friendly with and can work with. You want a wide range of skills (graphic artist, front end developer, back end developer, DBA) so that when the big contract comes along you're ready.
As you move from contract to contract keep in touch with these people. You're trying to build a network of genuine friends and business associates who can help you when you need them. Help them out with their projects before considering your own.
You want to fully understand the business of software development before you attempt a larger project that will require multiple people working on it. To that end, ask these people about their experiences. Gain and share knowledge.
Step 3 - Let your agent know what you can do
Big companies occasionally have large projects that they need a specialist team to work on for a period of time. They are seldom directly advertised. Rather they are put out to tender via the preferred supplier list of the company. There is almost no chance of you getting on the PSL without proven experience of similar jobs so you need to start small. This is where your agent can help you.
For small projects, agents are often tasked with finding multiple candidates. If you are able to say to your agent that you have an entire team ready to go that solves their problem. They can put your company forward as the solution and still take their cut. If it works out, everyone is happy.
Over time you build a reputation for delivering quality work and can afford an advertising and canvassing budget (warm/cold calls to large business) so that you can ease yourself onto the preferred supplier list for a large company. Once there, you've achieved your goal.