This is a highly complicated area of law that requires a professional's expertise.
Must have 10 years of Physical presence: Prior to the date of application you need to be in the US for 10 continuous years. That date begins when the alien enters the country and ends when they are served with a Notice To Appear or have committed certain crimes.
Must have good moral character during the ten year period: Generally you should have no criminal record. Examples of crimes that would negate good moral character are drug traffickers, multiple criminal convictions, or prostitution.
Exceptional and extremely unusual hardship to U.S. citizen or Legal Permanent Resident (green card holder) spouse, parent or child: This is by far and a way the most difficult of the three criteria to meet. Factors that are taken into consideration include:
Generally you will need documents from your home country to support your story. In addition it is recommended that you hire an expert who can corroborate your facts.