In Connecticut state courts, the rule is one day or one trial if you are picked for the jury. There is a phone number that you call the night before to see if you must appear. If you actually go in for the day and don't get picked, you're usually free from a call for the next three years.
Once you arrive at court, you are given a jury questionnaire to complete. It asks whether you or a member of your family is in law enforcement or is a lawyer, and a few other personal questions, such as place and type of employment. These questionnaires are given to the lawyers who will conduct the voir dire. You also watch a film about the court process and your potential role in it.
In the first step, all the people called for the day are herded into the courtroom and questioned as a group by the judge. This is designed to weed out quickly people who cannot be on a jury due to a variety of common personal reasons -- have child care responsibilities, or medical care for the elderly, or their own health issues, or work that won't pay them if they are on a jury, vacation plans etc. The ones with a valid reason are excused and the remaining people are then given an oath and become the venire (the pool of potential jurors.) They then go to another room to wait for voir dire.