Unless there's a specific show you're after, the best way to score discounted tickets in New York's Theater District is at the TKTS Booth, under the big red steps on the north side of Times Square. Same-day tickets for top Broadway and Off-Broadway shows are sold for 20% to 50% off. For the best selection, line up before opening time (3pm Monday, Tuesday and Friday, 11am other days).
Smartphone users can download the free TKTS app, which offers rundowns of both Broadway and Off-Broadway shows, as well as real-time updates of what's available that day. Always have a backup choice in case your first preference sells out, and never buy tickets from scalpers on the street.