Go to the box office of the theater that is hosting the show you want to see and buy your tickets straight from the box office with cash or debit or credit card. This is the cheapest way to buy tickets, but if you don't live in Manhattan or nearby, that may be a difficult option.
Call Telecharge or Ticketmaster (see resources 1, 2) or log onto their websites and find the show you want to see. Click "tickets" or "buy tickets," and you will be directed to enter your debit or credit card information, including the security code. Service fees will be added to your tickets, but they can sometimes be cheaper than buying from other vendors, as these two companies are often the "official" dealers of Broadway tickets.
Scrounge for returned tickets. When people can't make the show, they have the option of returning the tickets. Show up at the theater and go to the returned tickets line. If you get there early enough, you could be lucky and score last-minute seats to a sold-out show.
Look for tickets being sold on free classified listings like Craigslist. This is a bit like scalping, which is not recommended by anyone in the theater industry, but if you're desperate, it's a way to end up at the coveted show you've been dreaming to see.