How do I book a flexible flight ticket?

Assuming you mean flexible at the time of booking but "in stone" once confirmed, it's a pretty easy task. Since I do not know what airline you plan to fly, I will make this answer generic in nature. Below the departing and returning date fields, you should see a check box for "flexible dates". By clicking on this option, the fares for the selected dates will appear in a table, or grid. Typically the flexible days displayed are +/- 3 days before/after the chosen date. The departing flight would be, for instance, axis X (left hand column) and the return flight axis Y (across the top). The fares for each date combination are displayed within the grid. Find the flight that is within your travel budget then look to the top and the left to find the departure and return dates. Keep in mind that this display usually shows the lowest fares for the dates selected. The actual fares will vary based upon cabin class, departure times, whether the flight is direct or has a layover and fare codes. If you are unsure of the dates and there is a possibility you may need to make changes to a confirmed flight, you will want to read up on the fare codes as not all flights can be changed without incurring rebooking fees and/or penalties. For more information on airline fare codes, check with your preferred airline. I hope this answers your question.