This quest can be acquried from Huntsman Berthold in Rattay. Listen carefully to the imitation of the Nightingale song so that you know what to listen out for when searching for them. Once you are sure that you know the tune reasonably well, make your way to the woods (Vranik Forest) west of Rattay.
Once you have located a Nightingale by sight or sound, find the empty bird cages in your inventory (in the 'Other' category), drop one on the floor and step away from it. When the Nightingale song ceases it has successfully been caught.
Pick up the cage and repeat the process until you have caught all three Nightingales. Take note of where you wander in the forest; there are a number of bandit camps throughout.
With all three of the Nightingales caught, take them back to Huntsman Berthold to complete the quest.