I wrote this summary for a friend earlier in the year. Easier to cut and paste and you can choose which bits are helpful to you!
Musicals
I am assuming you want to watch a musical. Correct me if I'm wrong as there are plays on broadway as well. So the popular ones are still there. Mary Poppins, Jersey Boys, Wicked, Chicago, Lion King, mamma Mia, Phantom Of The Opera, Memphis etc. Buying advance tickets will set you back $100-$200 per ticket. Do this if you are set on watching a particular show at a particular time.
Other options:
1) Check for deals on the direct website of the production. Doesn't happen often for the popular shows! I checked the most popular ones for you already...
2) Broadway discount tickets online newsletters and websites. Once again you don't have time to stalk them for good prices.
3) TKTS Booth -
http://www.tdf.org/TDF_ServicePage.aspx?id=56
Typically you get 25-50% off full price tickets but you need to line up the day of the show to buy the tickets. And what they sell will be dependent on what's left. The choices though are usually decent. For example this was what was offered last week.
ANYTHING GOES
BARRYMORE
CHICAGO
GODSPELL
HOW TO SUCCEED
JERSEY BOYS
JESUS CHRIST SUPERSTAR
MAMMA MIA!
MARY POPPINS
MEMPHIS
ONCE
OTHER DESERT CITIES
PORGY AND BESS
PRISCILLA, QUEEN OF THE DESERT
ROCK OF AGES
SEMINAR
SHATNERS WORLD
SISTER ACT
SPIDER-MAN
THE PHANTOM OF THE OPERA
THE ROAD TO MECCA
VENUS IN FUR
WAR HORSE
WIT
4) Rush tickets at box office
Rush tickets are normally available either when the box office opens or a few hours before the production starts. Rush tickets are normally about $20-25 each. Sometimes a student ID is required to purchase tickets. Many times, box offices will only accept cash as payment for rush and standing room only tickets, so arrive at the box office prepared. With so many variables depending on the production and box office rules, the most accurate information can be found out about rush and standing room only tickets by calling the box office for the particular show you'd like to see. In my experience, they are very helpful and can even tell you which nights might be easiest for getting tickets.
In short, I'd recommend the last 2. First thing you must do is prepare a shortlist of the musicals that you are happy to see, say about 5 in order. The TKTS booth is often busy and people are impatient! Then I'd go to the TKTS site and make sure you're familiar with it. Where it is, how to buy tickets, where to line up, when it opens, etc. The Brooklyn one might be worth going to as it always less busy than the Times Sqaure one. The recommendation for Times Square is to get there 1 hour before it opens. Be aware that usually mornings are for matinee shows and booths open again at 3pm for evening shows.
Rush tickets are also worth it but a lot more work. Here is a good link on how to do it.
http://www.ehow.com/how_2064157_get-rush-tickets-broadway-show.html
Or if you don't want to wait in line and you don't want to do any work. Just buy full price...