Yea... it took me a while to figure this one out as well. You have to catch those little birds that are often seen on the surface with your net. You have to move slowly, though, because they are rather timid, and will fly away without hesitation. If you swing your net and miss, them movement will also scare them away, so the easiest way to do it is to Z-target the birds and just creep up slowly until they are within reach of your net.
You usually can only catch one bird per flock, since the sudden motion of swinging your net will scare the others away... however, they usually re-appear in the same spots if you just walk around for a bit. The blue birds get you the 'Blue Bird Feather', which is also an obtainable treasure for upgrading.