Check the Indianapolis Symphony Orchestra website for a schedule of Symphony on the Prairie performances, which run the entire summer and include shows with different themes. You can buy general admission tickets, which are good for a spot on the lawn, or you can spring for a reserved table closer to the stage.
If you don't want to bother with making a picnic, order a picnic in advance from the Conner Prairie catering department and pick it up when you arrive.
Pack up your other supplies. Many people who attend Symphony on the Prairie bring folding lawn chairs, but you'll be fine with just a blanket, too. If you have too much stuff to haul, bring a children's wagon to haul your supplies. Alcohol is allowed on the Conner Prairie property, so pack your favorite bottle of wine if you like.
Arrive at least an hour before the performance to claim your spot on the lawn and start eating. The exception is the Fourth of July shows, which are packed. If you're going to one of those performances, arrive whenever the gates open and bring your sunscreen -- you're in for a long day in the sun and heat, but it will be worth it at day's end.
Mind your manners during the performance, just as you would in a concert hall. It's OK to keep eating, but keep noise to a minimum. If you answer your cell phone or carry on a loud conversation, you'll get dirty looks from people trying to enjoy the music.
Clean up your mess before you leave. Trash containers will be all around the lawn.