Who likes paying high ticket prices for a Broadway Show? You can bet that I don't so I signed up at various sites to get emails for discounted show tickets. Usually they are for a show about to begin its run and only for a specific time period. I would also guess that if a show is not doing well or has been running for a long time, you may get emails for discounts.
You can print out the email and go directly to the box office for purchase or do it online using the code from the email. That's all you do, other than hope to get a good seat.
You can go to the TKTS booth in Times Square at Broadway and 47th street for tickets to a show that same day. For evening performances, tickets start selling at 3pm, and for matinees, 10am Wednesday and Saturday and 11am on Sunday. The line starts way before selling starts.
Sometimes you can buy tickets for "standing room only", or the box office may have "rush" seats, at a discounted price, at the very last minute.
Check out about.com and search "discounts for broadway shows" to get more information.
Just be sure to turn off your cell phone when the show starts!
Ticket sites: theatermania.com, playbill.com, nycgo.com (limited shows, but lots of other discounts,) BroadwayBox.com (a site to click for coupon codes for all shows,) seasonofsavings.com, to name a few.