Rush tickets are normally available either when the box office opens or a few hours before the production starts and are typically $25-35 each. Sometimes a student ID is required to purchase tickets (though often with one student ID, two tickets can be purchased). 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. Playbill's directory of Broadway shows is the most comprehensive/up-to-date I've found.
Playbill.com maintains a listing of rush and standing room only performances and guidelines that is very helpful.