The IRS has pretty strict standards on whether or not you are considered an 'employee' and the penalties are hefty if you are mis-classified. If you are working on hehalf of the company I believe you will be considered an employee for tax purposes. The s-corp WILL need to pay the matching taxes to what are deducted from your paycheck. Keep in mind that you will be deducting fed tax, state tax, ssi and medicare from your paycheck and the company will also be paying matching ssi and medicare as well as fed and state unemployment taxes. You will also need to obtain a worker's comp policy and you may wish to add company paid (at least in part) health insurance to the mix. The company will need to set up EFTPS deposits for the IRS and you will need to check with your State on when their tax deposits are due, as well as how to make them. You will also have to file W-2s at the end of the year as well as the 1099s.
I HIGHLY RECOMMEND YOU TALK TO AN ACCOUNTANT about setting up the tax reporting systems. If you don't have an accounting program in place, I suggest QuickBooks. Depending on the size of your s-corp it may make financial sense to purchase the annual payroll service from them. If you are a VERY small business, (1-3 employees) the payroll can be done by hand in a cost-effective manner. Otherwise, the payroll system is usually a good idea.
All that being said, the book I wrote "How To Do Your Own Small Business Bookkeeping" (link in signature) will walk you through setting up basic QuickBooks bookkeeping and also tells you item-by-item how to set up the taxes and how much/when to make tax deposits. My business is also a part-time option for bookkeeping services as most small businesses can get by on less than 10 hours/week of bookkeeping services.