The process of selecting a jury is known as voir dire. During voir dire, a panel of people will be questioned by both sides about their background, beliefs, and biases. The jury will be selected from this larger panel.
Each side has an unlimited number of challenges for cause. Usually, a challenge for cause is made when one side believes that a prospective juror has a bias against them. For example, a prosecutor in a capital murder trial might challenge a prospective juror who says that she objects to the death penalty because of her religious beliefs. The defense attorney might challenge a prospective juror who says that he believes that any defendant who does not testify is guilty. Such a point of view contradicts the Fifth Amendment of the Constitution.
Each side may make a limited amount of peremptory challenges. A peremptory challenge does not have to be explained. That is, each side can simply strike a certain number of prospective jurors from consideration. The amount of peremptory challenges varies according to the type of trial and the number of defendants.
In the typical felony trial, each side is entitled to ten strikes. In the typical misdemeanor trial, each side is entitled to three strikes.
There is one exception to peremptory strikes. The state may not make strikes based on race. That is, the state may not strike African-American or Hispanic panelists because the defendant is the same race or because the prosecutor believes that minorities are soft on crime. When a defense attorney believes that the prosecutor may have made improper race based strikes, he will make a Batson challenge. A Batson challenge (named after the U.S. Supreme Court case that forbids race based strikes) requires the prosecutor to show that his strikes were not racially motivated.