Go online and visit the home pages of major airlines such as Southwest and United. You should also check discount airline websites such as Travelocity and Priceline to make sure you have researched as many places on the Internet as you can. Type in the date you're leaving, when you're returning (if you are), and the times you're willing to leave. The results and accompanying fares will come up on your monitor.
Call the departure airport directly and ask for the currently available Y-class fares. Those working at the airport can pull up the fares that meet your requirements and give up-to-the-minute figures on availability and prices. You can also ask the person how many seats are currently left, and even where those seats are located, to see how much room is left at the Y-class fare level. If you've already checked Internet sites, you can compare various fares to see which one suits you best.
Purchase the fare that you want. It's important that you check all of the options and that you're sure of the times, dates and all details. If only a small number of Y-class fare seats are available, purchase your ticket immediately before the fare could be taken by another person or go up in price.