Rensa is the man standing in front of the stable and is the twin brother of Tasseren, who runs the stable. If Link speaks to Rensa, he can ask him for directions to various locations and can talk to him about Wild Horses. After speaking to him about Wild Horses, you can talk to him a second time and he'll offer Link a challenge to take place in the Hyrule Horse-Taming Competition.
In order to complete the quest, Link must find a Wild Horse, tame it, and ride it back to the stable within the two minute time-limit. Rensa will point Link in the direction just southeast of the Dueling Peaks Stable, towards the Bubinga Forest, where there are a number of wild horses.
There are multiple ways for Link to mount a horse. Either he can kneel down and very carefully sneak up, using stealth to not scare the horse. When he is close, he can jump on its back. Usually the horses that are solid colors are harder to tame and Link may need to repeatedly tap 'L' to sooth the horse. The spotted horses are much easier to tame and work best for this particular mission. Alternatively, Link can paraglide from a higher point and try to land on or right next to a horse. Link can also just run after a horse, sometimes chasing it towards the river where it has nowhere to go, allowing Link to quickly mount the animal.
After mounting a horse, simply ride back to the stable and Rensa will automatically talk to you. Link's reward for completing the quest in less than two minutes is a Purple Rupee.