How can a person apply for a visa since they have entered the country illegally and have lived here for over 8 years?

Anyone who has been out of status in the US for 1 year or more is barred from entering the country legally for 10 years.  A waiver is available if the person can show extreme hardship to a US citizen spouse or child.  Right now, the person seeking such a waiver must apply for the waiver at a US consulate outside the US.  Regulation is pending that would allow someone to stay in the US while making such a waiver request.  However, without a US citizen spouse or child, there is little chance of regularizing status.