-Go to the closest US Embassy in your country (including Canada and Mexico) and request information regarding a visa to either live and/or work within the United States.

-No company within the US is to hire anyone, in any capacity, i.e. driver, secretary, mechanic, etc... who does not have an Employment Authorization Document (EAD) or proof of US citizenship or a Permanent Resident Alien Card (green card).

-The Immigration and Naturalization Service can enter a place of employment, audit all employee records and place a hefty monetary violation against any company who hires anyone who does not have official authorization to live and work inside the United States. Each employer is to maintain INS Form I-9 on file for all employees noting (or keeping a copy) of what official documentation was presented as proof of lawful residency or citizenship.

-It is possible that drivers may have a hard time obtaining a visa based on the occupation of "driver" since many of the work visas are for the more highly technical skilled, but there are some visas available for unskilled or lesser technical nature, but you won't know unless you ask.
Footnote from lady I spoke with:

-You may have a family member who qualifies and can petition for you and you may not be aware of it. It would seem that it would be a black mark against you and a company if you were booted out (new word in Immigration is now called "removed" from the United States. Don't take chances and get the proper work documents before applying for a job. Don't waste your time and the ones trying to hire those in a legal status or US citizens.

-US providences that are a part of the United States-NOT part of the mainland and the driver has not driven stateside:   You will need training for the US.  Insurance companies require that you have United States training as the conditions of the roads, traffic and laws are different to some degree.  No different than military drivers needing civilian training. 

-More in-depth help for the immigrant worker:
Hammond & Associates

MILITARY DRIVERS GOING INTO CIVILIAN DRIVING

-Drivers coming out of the military who want to continue driving as a civilian must be trained to drive as a civilian  driver.  Seek a good school or carrier owned academy to get your civilian commercial license and training before wanting to be hired by a civilian carrier.