Quote from Vinny1:
How would a self employed person go about paying unemployment compensation taxes?
Easy. You make youself an employee of the company therefore paying taxes like any employee. People in the construction business up north do this because they're often out of work in the winter, but they can collect unemployment until it warms up enough to work again.
Btw, with respect to unemployment, when you consider that the majority of people under say 25 or so are virtually unemployable it's amazing the numbers aren't higher.