I found a link to the IRS website that helps a bit. Just Google "contract employee taxes" and the IRS link should be the first one to pop up. It seems that first you have to determine if you are an independent contractor, an employee (common-law), a statutory employee, or a statutory nonemployee.
A few paragraphs down it actually says that an employer can be held liable for "Misclassification of Employees" and therefore may be "held liable for employment taxes for that worker."
The only problem I found is that an instructor can be called a statutory nonemployee if... "Their services are performed under a written contract providing that they will not be treated as employees for Federal tax purposes." And I signed that contract. Lovely.