The mist nets are so fine that most birds don't see them before they hit them. There are also pockets that run the length of the nets and the birds often fall into them. Sometimes some feathers get rumpled, but a little preening will fix that.
Here an American goldfinch male (already getting yellow and putting on his dark cap) hangs in the net, probably trying to figure out what just happened.
The bird is carefully extracted from the nets. The banders always do this part bare-handed so they can always monitor exactly how firmly they're holding the birds. This is one way they prevent injury to them.
Once free of the nets, the birds are placed in cotton sacks until it's time to collect the data.
Typically, it only takes at most a handful of minutes between the bird hitting the net and the release after processing.