The Delacorte Theater can be found just off of 80th street on the southwest corner of the Great Lawn. Tickets to shows at the Theater are free, so long as one is prepared to wait in line on the day of the performance to obtain them. Shows are announced usually in early winter, but the schedule is posted early spring More information can be found at the following link:
http://www.centralpark.com/guide/attractions/delacorte-theatre.html