Top tips for booking an award ticket:
Book early (330 or 331 days in advance depending on the airline, when the airline first makes seats available through their computer reservations systems), or book late (within two weeks of travel, when airlines may release unsold seats for mileage redemption).
Be open to traveling at off-peak times for where you want to travel. Trying to book Orlando or Hawaii at during the Christmas busy season will be tough.
If you are using American Airlines’ award points, monitor their list of recommended award destinations (such as American’s AAdvantage HotSpots These are routes with lower demand and more unsold seats, and therefore your odds of successfully redeeming miles is greater. United Airlines’ website has a list of destinations where they have additional space available for award travel.
Look at airline partners for opportunities to book award tickets (for example, American Airlines partners with British Airways, Mexicana and more, Delta partners with Air France and more). Trying to find 3 or more award seats on the same flights (for family travel) is next to impossible. Either split the family up to take two different flights or book award tickets for one or two tickets and pay for the other seats.