It varies a lot depending on where you are. In Australia, it's dead easy if the employee has a registered business number (ABN) to be able to contract as a 'sole trader', because they can just give you a tax invoice and declare the income separately when they do their tax return (it's just a separate section on the web form).
But probably only 10-20% of people will have set that up, and for people who don't have an ABN, you have to basically fill out all the forms you would to make them an employee (you need their tax file number, have to submit a form to the tax office, have to get their superannuation details so you can pay them the mandatory 9% additional retirement savings on top of what you pay them, etc.)...
But probably only 10-20% of people will have set that up, and for people who don't have an ABN, you have to basically fill out all the forms you would to make them an employee (you need their tax file number, have to submit a form to the tax office, have to get their superannuation details so you can pay them the mandatory 9% additional retirement savings on top of what you pay them, etc.)...