How can I witness a United States Supreme Court session?

I went on a day with a fairly boring case and showed up around 7:45am. I waited in line for many hours and missed the entire first argument. I made it in for the last 30 minutes of the second argument (around 11:30am). It was a great experience but I was really close to not making it.

At first there is only one line that you can get in. I would recommend getting there as early as possible but not later than, say, 7:15am. Once the time gets close to around 9:30am there will be an announcement and the formation of two lines. The line you are already in will be for a permanent seat in the hearings. The new line to your right will be for quick 3 minute visits into the hearing. Hopefully, most of the people in front of you will move over to the new line and you'll be more likely to get in.

After that a set number of people from the permanent line will be let in. There was surprisingly little turnover after the first argument ended. The process of getting is also very slow, with multiple metal detectors, instructions, locker stop, etc. If it's getting close to the end of the first argument and you're not within, say, the next 30 people in line I would jump to the temporary line and at least get a few minutes in the court. Keep in mind, you can jump into the temporary line at any point. Also, you can get right back in the temporary line when you're done with your 3-5 minutes. It also seemed like some of the temporary line people stayed in significantly longer than 5 minutes, so this might be a good option if your desperate.