What happens in jury duty and how long you serve is largely dependent on state requirements, but in general at least here, you fill out a questionnaire, are paid money when you show up, and you will be sitting for a week. Any time in that week you may be called as many times as they like (you are usually required to call a number each day to see if you are required), but in my experience it's only once. It is hard to get out of jury duty in our state and particularly my county. You can only delay it, unless completely exempt. Usually it ends up in a plea deal and you get $30 for several boring hours of sitting. On occasion someone for the county will try and coerce you to donate that money. Sometimes you do get as far as voir dire, and you'll be asked a long list of questions that you may or may not agree with or if you know about the case in question. For me I was called to stand before the judge and the accused and was asked questions regarding the overview of the case, my feelings about guns, property rights, and if I had been a victim of a crime. I was not a candidate, based on my answers to serve on the jury, and was dismissed from service. If you serve your allotted time, you will not be called again for a designated amount of time.
Like you, soon after he naturalized, my husband was chosen for jury duty. He was actually quite excited about it, but after sitting for three hours the judge dismissed him for the day. There was then an emergency at the courthouse, so court was cancelled for the rest of the week and so was his term of service. The main thing is to always answer truthfully, make sure you know the rules of what you can and cannot bring inside, and of course certain answers don't usually make you favorable to sit on a jury.