It isn't necessarily something you 'start up' unless you're talking about a legal tax status.
A lot of employers get around tax regs by hiring "temporary" labor -- by the week, or the month, whatever, without defining them as "employees". They pay that temp labor a lump sum, with no tax withholding -- which might be a nice chunk of change in the short term, but at the end of the year that labor gets a 1099 form (instead of a W-2) which becomes a major headache unless you really like filling out obtuse tax forms, and where you literally have to tax yourself.
Actually you're expected to send the IRS "estimated" tax four times a year if you do this regularly, although that, in typical IRS "wisdom", expects you to actually predict the future in order to estimate it.
I worked this way for about 30 years. When I did I would use the term "independent contractor", "consultant" or "freelancer" interchangeably, though I never actually founded my own company. It has its benefits and drawbacks. Biggest benefit is, by definition your job has a finite end, which not only frees you from the insufferable chains of Monday-Friday 9-to-5 Routine Hell, but gives you a finite end to the task with a sense of accomplishment at the finish line. The taxes are no picnic though.