No, you'll still self-employment taxes (the self-employed person's version of Social Security/FICA taxes), but they'll be based on your profit--if any--as calculated on Schedule C.
Let's say you've got a job at a company that pays $50,000 a year. You pay Social Security (FICA) on that $50,000.
During your spare time, you create a Web site that earns $10,000 in revenue from AdSense, affiliate sales, or whatever. You declare that $10,000 on Schedule C, on which you also list $1,000 in legitimate business expenses: domain fees, hosting fees, related software, the "How to Become a Web Millionaire" book that you picked up at Barnes & Noble, home-office expenses (though these can be trickier), etc. The net after deduction of expenses, or $9,000, is your profit. You pay self-employment and income tax only on that profit, not on your gross revenues before deduction of business expenses.
Again, TurboTax or TaxCut will make it very easy to figure all this out. You just answer questions in an interview, and the program does the calculations on the proper forms.