Re: WhiteHouse.com ... A zero-day is a computer-software vulnerability either unknown to those who should be interested in its mitigation or known and without a patch to correct it. Until the vulnerability is mitigated, hackers can exploit it to adversely affect programs, data, additional computers or a network

Nonetheless, finding a 0day makes you a c00l d00d. There are a number of known ways to find 0days. Basically you mess with software until it crashes, while running it under a debugger. You can also analyse code in depth to find it; this is likely easier if you've already found some to get to know stuff. You also want to stay up on new exploits, cause often entire new classes of 0days are revealed, and each time you can scrube every product in existence to find other similar 0days. So basically our planet is run by whoever has the balls to hack into every device.