How does a good idea turn into a successful business?

My roommate and I just came up with what we think is a good idea for a website/business, and that got us thinking about how the big successful companies we know today got their humble starts. Both of us are in college for science related degrees, so neither of us really knows a whole lot about economics or management, and we're definitely not thinking about trying our hand at business. But it got us curious. Is there a general process that takes a good idea, turns it into new company, and grows it into a successful business?