This task is unlocked during the main quest Family Matters. It is given by the Pellar (M3,7).Before you start looking for the goat, open the inventory and move Pellar's Bell you've received to the active inventory slot. Now pick it from the quick choice menu so that pressing the correct button/key will make Geralt use the bell.
Enter the territory marked with yellow circle and start using the bell and witcher senses. You must be on guard as Geralt can be attacked by wolves during the search. The goat can be found on the west side of the forest (M3,8). Use the bell to make her follow Geralt. Don't go too far away from her or she will lose interest in following you. The goat will walk out of the "path" few times and, in one case, will go close to a bear cave. When fighting the beast, try to avoid its attacks and perform strong attacks. It is a good idea to use beast oil before the battle. You must guide the goat to the Pellar (100 experience points), it will allow you to continue the Family Matters quest.
If you don't want to risk fighting the bear near the protected goat, you can first go to its nest, before you find the Princess. Starting with dealing with the bear will make it much easier to guide the goat to its owner.