What restrictions does the eight amendment place on bail and punishment?

Amendment 8: "Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted."

It basically means that "the punishment must fit the crime". Punishment and fines need to be reasonable (you can't sentence someone to die for stealing a bicycle from someone). And the court cannot set bail at an amount that is more than necessary to ensure the person will be in court on the day of their trial.