Each state sets its own policy about selection of justices for its supreme court. Some follow the US example, with the governor nominating candidates and the state legislature voting to approve or reject. Other states follow something called the "Missouri Plan," in which a special Committee presents three potential nominees to the Governor, who either chooses one or defers to the Committee selection. The justice is then appointed to a temporary one-year term, after which he or she must be reconfirmed by popular vote in a general election every X-number of years. Some states use the popular vote exclusively; in those cases, the state determines whether the candidate may be affiliated with a particular party, or whether he or she must run as a non-partisan. Some states use general election processes (both partisan and non-partisan), and there may be other variations.
The question is really too general for more specific details; for more information, please specify the state in which you're interested.
They are nominated by the president and confirmed by the Senate.
It varies by state. Some places they are elected, in other states, they are appointed by the governor.
The president selects the judges in the Sumpreme Court.
the president
Congress has to approve the US Supreme Court nominees.
The president selects the nominees for his cabinet, including the secretary of defense.
They hold the hearings to determine the nominees of the Supreme Court. There have been six nominees that the senate has rejected over the past sixty years through this process.
Both nominees had supported segregation in the past
Both nominees had supported segregation in the past
Senate.
The American Bar Association issues an opinion about the professional competence and qualifications of US Supreme Court nominees and potential nominees.
Selects judges
The US Senate confirms SCOTUS nominees.
Supreme Court nominees often evade questions related to ideology; how they would rule in hypothetical cases; state their opinion about controversial settled law; or indulge in conjecture that might unfairly effect their chance of confirmation.
The American Bar Association (ABA)
The man freed slaves. Thats a major one right there.