Birds that have trouble breathing will often breathe with their mouths open, seem "puffed up" or have trouble staying on their perches. Some birds may even tail bob, where the tail moves up and down with every breath, if breathing requires a whole body effort. In some birds, a squeaking noise can be heard with every drawn breath. Birds have an extremely efficient respiratory system and generally do not develop breathing trouble until a disease is well advanced. Any bird that appears to have difficulty breathing should be seen by a veterinarian.
For more information, please read the article Dyspnea.