When you need to catch a bird in an aviary, it is much easier to take down the perches running accross the flight first. This should prevent the bird from flying immediately out of reach.
Always use a well-padded net, to minimise the risk of injury, but take care not to wave it wildly at a bird in flight, as this could cause serious harm. It is much better and often easier to net the bird when it is resting on the mesh.
In the case of species such as quails which normally spend most of their time on the floor of the aviary, beware because they will often fly up vertically when frightened, with the result that they are likely to collide with the roof of the aviary, damaging their heads. Try to shepherd such birds into a corner of the aviary, where you can stand over them, so they will be less likely to fly upwards. This will reduce the likelihood of injuries.