Use an online travel website such as Priceline, Orbitz or Hotwire to book your air tickets. Type in the dates you are leaving and returning and these websites will pull up all the deals and prices from all airlines. You can shop all airlines in one place and pick the best deal. Check into packaged deals as well. Even if you may not need a hotel or other transportation, these packages may save you money on airfare.
Book directly through an airline's website. Use the reservation option and add the dates of when you are traveling. Pick the flight that best fits your schedule and confirm the flight.
Contact a travel agent if you are not comfortable booking an air ticket yourself. Meet with a travel agent to discuss your travel plans and he can book you a trip with the best timing and price for your needs. Often airlines offer specials to travel agents you cannot get in other places. If you don't have time to meet with a travel agent, there are a variety of agencies that work solely over the Internet. These agents communicate via Skype, email or the phone.