@gollum,
As a general rule, a state can't be sued. That's what's called "sovereign immunity." In certain instances, however, states will waive their sovereign immunity.
If you sue a state, it's usually only in a special court, called a "court of claims." These types of courts typically don't have juries.
If the state loses at the trial court level, it can appeal. If the plaintiff is dissatisfied with the amount of the award, he or she can also appeal.