Along with the snare, you get some advice on crane hunting:
The greatest cranes of the Krasarang Wilds don't care about simple things like food. You need to play on the creatures' emotions if you want to draw them out of the jungle.
There's plenty of cranes on the Cradle of Chi-ji and on the Narsong Spires, both to the west of here. Pluck some of those cranes' quills, then put them in a visible spot near the Crane Temple. Your quarry will come running to you.