Legendary Pokemon are powerful, usually high base-stat Pokemon. They can be a valuable part of many teams. They tend to be difficult to catch due to a low catch rate, however, they are usually valuable parts of many teams.
Legendary pokemon spawn very rarely, and in their own specific biomes. Some legendary Pokemon do not naturally spawn and must be created. The three birds (Articuno, Zapdos, and Moltres) must be spawned by filling an orb and then the orb must be used at a shrine. The Mewtwo is spawned by inserting a Mew into a cloning machine. Here is a list of the biomes in which the legendaries spawn as of 5.0.4.
All legendaries have a catch rate of 3, apart from Celebi and Mew, who have catch rates of 45. This means that most legendaries are difficult to catch. A good strategy for legendaries is to use Timer Balls, as timer balls will have a 4x catch rate after the 13th ball. Fast balls are good to use against Celebi and Mew, as they both have a base speed of 100, which allows fast balls to be effective. You do not need to damage Celebis or Mews, or use Masterballs on them because they are very easy to catch. Below is the chart of the most effective ball to use for various Legendaries.
After the 13th turn into a battle, Timer Balls will always have a 4x catch rate! Thus Timer balls are by default one of the best balls to use for all legendaries besides Park Balls and Master Balls, which both have a 100% catch rate. Dusk Balls are also very good, with a 4x catch rate during night time.