Taming is the method of capturing a monster without monster-to-monster combat. If a monster is successfully tamed, it must be taken to the herd keeper where the player can then interract with the monster to further gain its trust.
To capture a monster via taming, the player must have special one use taming crystals that will store a monster's essence and molecules (it isn't just an essence, it's a real monster trapped in the crystal). When the player is close enough, a crystal is automatically filled from the players inventory. Once filled, the crystals cannot be sold. If the player has no taming crystals, they may not attempt taming.
To catch the monster the player wishes to tame, he must right click the mosnter and select attempt to tame. The player will automatically approach the monster's range and taming will begin. Taming cannot be attempted while in combat which means a player must select the tame option outside the mosnter's range. Turns work like combat where your turn bar fills up etc. On your turn, you can choose to sneak or throw it an item (any item from your inventory). Different monsters have preference to specific types of items, and then each monster will randomly have a favorite item within that preference type. Throwing a bad item will make the monster more frightened. Sneaking closer will increase its nervousness but the player must be close enough to successfully tame it. After the player takes his turn, an animation will play indicating the monster's level of trust: a series of twitches/shivers (nervous), contented swaying/sigh (trusting), no animation (neutral). If the player fails to tame the monster, and it becomes too nervous, it will run off into the closest spawn area for that monster.
After filling his taming crystal, the player can take it to the herd keeper. The herd keeper will let the tamed monster out into his ranch where the player can enter the instance to play with his own monsters, decorate the ranch, feed his monsters, etc. Certain items will provide extra bonuses for the monsters when placed in the ranch. Playing with or feeding a monster will also increase their trust in their owner; however, play and feed actions can only be used a certain number of times a day. Players can also train their monsters in various minigames like timed laps, obstacle courses or sharp shooting ranges.
The rewards for fully trusting tamed monsters is that monster's ultimate skill. The type of skill will vary among monsters (attack, healing, passive, etc) but is not unlockable in any other way. Once the monster is tamed to full trust, all other monsters of the same species that the player owns can buy the ultimate skill with skill points (given the monster meets the appropriate prerequisites).