A corporation is a legal entity which is independent of its owners. To incorporate, you must fill out articles of incorporation and file them with the appropriate state office, and pay any fees.
A corporation always starts as a C corporation, which is subject to federal income taxes on the entity level. An entity becomes an S corporation after filing the appropriate form (2553) with the IRS. The net income is passed through to the shareholders and included on their personal tax returns, thus avoiding the corporate double tax.