What DemonSpawn said, in a nutshell. You have to be a permanent resident for 5 years before you can apply for citizenship (unless you’re married to a U.S. citizen, in which case it’s 3 years).
The extremely condensed verion (if you have more specific questions, I’ll try to answer them):
Most green cards are based on close family relationships to U.S. citizens or permanent residents, and have annual quotas; most of those categories are seriously backlogged, by several years or more. There are a few green cards for refugeees/asylees, which from your description sounds like a category that won’t apply to you.
Then there is the employment-based category. Most employment-based green cards are for people with university degrees or the equivalent, who are employed in what the U.S. considers to be shortage professions, i.e. there aren’t enough U.S. workers for the job. This area of law (which is what I do) is extremely complex, and changes all the time. It used to be, for instance, that anyone working in the IT field could pretty much find an employer that would sponsor him for a green card, and if you could just wade through the bureaucratic hassles, you’d get it in the end. Over the past year or two, though, that’s been getting more difficult, as there are more U.S. workers available due to the economic downturn. Consequently, employers are less willing to hire foreign workers and/or spend the cash for legal fees and required job advertising for a green card, and the government agencies involved (INS and various state labor departments) are less willing to believe that sponsoring companies are unable to find U.S. workers.
The categories for most non-professional workers (not to insult what you do, but if it doesn’t require a university degree or the equivalent, INS doesn’t usually consider it a professional position) are so backlogged that in practical terms, they’ve been unavailable for years. There are a few wacky categories where the usual proof of an available, otherwise unfillable job with a U.S. employer doesn’t apply, but they are generally for people who do things like win Nobel prizes or are at the very tip-top of their fields (arts, sciences, business, etc.) and have all kinds of nontraditional credentials or awards to prove it.
Sorry to rain on your parade, but it sounds like your best prosepct is either to fall in love with a nice American woman, or you can always try the INS lottery (called the Diversity Lottery; it grants about 50,000 green cards a year, and almost anyone can apply). The odds are long, but I personally know 3 people who have gotten green cards this way (one of whom is now an attorney with my office), so it’s not hopeless.