Go to the website for the airline you want to use. If you do not have a preference, you can search a website that compares flights, such as Orbitz or Expedia.
Type in your departure and return dates as well as how many tickets you need to buy. You will also need to choose which airport you will depart from and return to.
View the results and choose the flights that best fit your schedule and budget. Some things to consider are the times of the flights as well as whether the flights are non-stop or if the flights have stops before the final destination.
Reserve the tickets by entering your credit-card information and responding to the rest of the prompts. Make sure you print confirmation of your reservation.
Call the airline directly if you have frequent flyer miles you want to use to reserve your airline tickets, or if you would rather speak to a human to reserve your tickets.