If a person works as a part time "Food Demonstrator", are taxes withheld or does one have to pay own taxes?

It sounds like you will be an Independent Contractor, hired to do that on a part time basis. You should get a 1099 form although if you make under $600 in a year they aren't required to send you a 1099--but you are still required to report the income on your taxes.

Regardless of whether you are part-time or full-time, you are either an independent contractor or an employee. If you can work at your own schedule, use your own tools and materials, then you would probably be considered an independent contractor. If you work according to the employer's schedule, using his facilities, tools, materials, you would be considered an employee. If an employee, then the employer must deduct federal and state income tax. In addition, the employer must deduct one half of the cost of your medicare and social security tax and the employer must pay the other half of your medicare and social security tax. If you are an independent contractor, then you will be responsible for paying all of the above taxes.

I agree. The way that you would have to pay your own taxes is if you claim self-employment. If you do, save all your receipts so you can claim as much as possible. If your company takes out your taxes, then don't worry.