I know people keep mentioning the TKTS booth but you would honestly be better off with BroadwayBox.com.
Go to the site, choose the shows you want and see what discounts are available for your dates. Write down the code for each show or print out the discount and bring it to the box office.
The reason I say this is because you'll almost be able to choose your own seats and likely get much better seats than from TKTS.
I've always had great success with the BroadwayBox discounts. One time, my daughter wanted to see a particular show. I got the discount code and went to the theater already having decided what seats I would want. The ticket person told me there was no way I could get any of the seats I wanted and that all orchestra seating is sold out for the next 2 months or so. As we were going back and forth over various seating, he tells me "you're not going to believe this. Two seats JUST opened right behind the original seats you wanted" and we booked the seats and got a 40% discount!!
We've seen so many shows with the BB discounts and have always gotten amazing seating.
You can also look at ILoveNYTheater.com --- they will tell you what shows have "lottery" and student rush tix (with valid, current student ID). Lottery is great (we've seen Wicked twice that way!!!) but you can only buy 2 tickets (same with student rush)
Lottery: About 2 hours prior to show time, you line up and put your name on a slip of paper and put it in a barrel thing. About 1.5 hours prior to show time, they spin the barrel and pull out 12 names. If you're one of the lucky 12, you have to show valid ID and you can buy 2 tix ($26-$30 each). They're typically orchestra seating, possibly first row. Cash only.
Student Rush: You show your student ID at the box office, you can buy 2 tix at discounted rate. Cash only.