At the end of the game, the laser turns blue and damages Calamity Ganon. When completed, a Divine Beast will shoot a red laser at Hyrule Castle. Vah Ruta is boarded by shooting it with shock arrows, Vah Medoh is boarded by landing on it after destroying it's shield, Vah Rudania is boarded by sneaking past and shooting Yunobo at it, Vah Naboris is boarded by preventing it from moving by shooting it's feet with shock arrows. Once you complete them, you will get a Heart Container, and a power from the champion who piloted it. You have to find and activate terminals, then fight a Guardian. You then find a map once you reach the Divine Beast. Each one has to be weakened before boarding them. Impa tells you about them when you reach the village.
They can be done in any order, but the easiest is: Ruta, Rudania, Medoh, Naboris. Lanayru has Vah Ruta, Hebra has Vah Medoh, Death Mountain has Vah Rudania, and Gerudo has Vah Naboris. The beasts are located in Lanayru, Hebra, Death Mountain, and Gerudo. To take control over these, Link must go to 1 of the four regions that their in. Link has to go inside and activate the terminals, then fight a Guardian.
The Divine Beasts are ancient creatures controlled by Ganon. Warning: This page contains spoilers for The Legend of Zelda: Breath of The Wild