You will learn about the quest from the notice board in Fyresdal. To receive more information you must go to the elder of the village - Vagn (M14,6). Before accepting the contract, you can bargain the price. Vagn should agree on 300 crowns. After you agree on the price, ask him about the monster. You will learn that two hunters have been killed but not buried yet.
Go to their home to take a look at the bodies. After you do that, go to the plain before the village. You will find a dead cow there. Follow the trail of her blood until you find a dead dog. High grass makes tracking harder, so keep attention to the ground lest get lost. After a while Geralt will see a Forktail nest on the high tower. To start the battle you must prepare a bait.
Go back to the elder of the village. He will give you a sheep that you must round up under the monster's nest. After you do it, a dragon will fly to you. Defeating him is similar to fighting other monsters of this kind, like wyverns. Use Quen sign to block enemy attacks and use crossbow to get him to the ground. You can also use Aard sign from the close distance. After you defeat the dragon, take valuable reagents and trophy (5% more experience for killing monsters) from his body. Go back to the elder for your reward.