This was a great question in class. The answer – – you might have guessed – – depends on the state.
Some states appoint judges in a manner similar to the federal system. For example, in New Jersey the governor nominates judges for confirmation by the New Jersey Senate.
In some states voters select judges. For example, in the state of Illinois voters choose judges through general elections. But Illinois also has “associate judges” who are appointed by judges to hear certain types of cases.
In Missouri and other states a judicial commission prepares a list of potential judges for the governor to review. The governor should select a judge from this list. In some states there is a general election after one-year to determine whether the judge selected by the governor should serve the remainder of his or her term.
New York (where I’m from) has an especially complicated court system. Our method to appoint judges is a bit tricky, too, and somewhat controversial. New York’s major trial level court of general jurisdiction is called the Supreme Court (remember, this is not the same as the Supreme Court of the United States). New York’s Supreme Court judges are selected by delegates from political parties. Some people consider this process unfair to potential judges who do not have political connections. You might find this case interesting.
In New York a commission nominates intermediate appellate level judges and the governor selects judges from the commission’s list. The governor nominates judges to New York’s highest court (called the Court of Appeals) for confirmation by New York’s Senate.