I'd start by reaching out to people that you already know through previous jobs and any other contacts you have (maybe avoiding people connected to your current employer).
Starting up a business is pretty simple from a paper work standpoint and doesn't have excessive overhead costs or paperwork requirements if you aren't doing any work through said company. Now you have a company ready to accept checks or payment when the work arrives.
in the US, most states allow an LLC formation - this is usually cheaper and offers you some protection against losing your personal assets in a legal dispute. You need to be above board and document all your stuff (expenses, etc), don't mix personal and business use expenses, keep separate bank accounts, etc. To start with for most solo freelancers, this is fine. At some point - "incorporating" might make more sense, but the ceiling would be moderately high. Going for an actual 'incorporation' may make more sense if you have external shareholders and such, or are looking to take investment from outside. Until then, as a solo practitioner, an LLC is usually the simplest combination of protection and minimal legal record keeping.
Starting up a business is pretty simple from a paper work standpoint and doesn't have excessive overhead costs or paperwork requirements if you aren't doing any work through said company. Now you have a company ready to accept checks or payment when the work arrives.