Currently the only way to get a green card if you are an H-1B holder is if the employer of the visa holder is "willing" to sponsor him for a green card after 6 years of employment. H-1B visa holders are professionals with Bachelor or Master's degrees on a special occupation, who pay taxes, consume goods, buy houses and invest in their education during their stay in the United States.
During their employment, employers can sponsor this visa the first time for 3 years and they can sponsor a second term for another 3 years as an extension. After the 6 years, the H-1B visa holder MUST return to their home country unless the employer sponsor their green card, this just happens if the employer is "willing" to do it.