Am I going to get hit with tax penalties?

I am 28 and work as an independent contractor doing web development for various clients. Because I do not have a traditional boss, no taxes are taken out of the checks I receive. I know I am supposed to send money to the government throughout the year, but I do not know how to calculate the correct amount. I am terrified that I will owe a massive penalty when April comes around. How do I get on track with these payments?