I know most US medical schools require you to sit the MCAT (entrance exam).
Medicine is taught at graduate level, lasting for 4 years.
You apply through the AMCAS website application service (like the UCAS in the UK) if you want to apply for the M.D. programme.
The MD curriculum might vary. UCSF outlines theirs:
UCSF School of Medicine - Admissions
Their website has got loads of info about other things too. Telephone them if you want more details.
USA also has a D.O. (doctor of osteopathy) programme which also leads you to becoming a doctor in the US. I heard that D.O. schools are slightly easier to get into than M.D. ones.