It's been a long time since I actually worked with non-U.S. citizens but my recollection is that there are at least three options:
- Work illegally.
Win the lottery for a green card.
Have your potential employer do the paperwork that essentially gets you a work visa because they are willing to claim they could not find a citizen/legal resident with the necessary qualifications.
The latter can be time consuming and somewhat of a joke. The employer pretty much writes a job description that is impossible for anyone else to fill, advertises it for a week and then claims there is no one qualified already in the country.
I'm kind of fuzzy on this but I think if you are here on a student visa there are circumstances under which you can work while trying to obtain a work visa.
Good luck.