Summarize:

The towel or net will help contain the bird as long as you use a gentle but firm grasp to hold the bird in place. A towel can also protect you from the bird while providing some calming darkness. Try to corner the bird first before dropping the net or towel over it. Grasp the head between your pointer finger and middle finger, holding it in the crook of your fingers up near your palm. Wrap your other fingers around the bird's wings to help keep it still. Be wary of the beak as you get the bird in this position. It's best to let an experienced handler or rescuer deal with a large bird if you're not accustomed it, as it can cause you serious injury. If you must handle one, wrap a hand around each wing to hold the bird in place. Try to keep the head in place by gently using your thumbs to steady it. When handling a bird, you do need to grasp it with a firm grip to keep it from struggling. However, make sure it's not having trouble breathing or squawking from pain due to your grip. A towel can provide some protection for you from the claws, and it may calm the bird down. Be gentle but wrap the towel around the bird and hold it in place. You can even put a towel over a bird's head as long as it is light enough for the bird to breathe through it. The longer you hold and examine the bird, the more stressed the bird is going to be. Evaluate the bird as quickly as you can and release it or move it to a box. Cut holes in the box to make sure your bird has room to breathe. Set the bird inside the box, and put the lid on. You don't need to add light, as the darkness will calm the bird down. A shoebox will work for smaller birds. If the bird seems very agitated or even somewhat paralyzed, darkness will help it calm down. Once it's in the box, place the box in a dark, quiet area to let the bird have time to recover. A light fabric will provide semi-darkness, but it will also allow the bird to see out a little. That can help keep some birds calm when you are taking the bird to the veterinarian or a rescue. For instance, cut a small hole in the side so the bird can see but cover it with a thin t-shirt. Don't make the holes so big that the bird can get out. If the bird is wild, a local wildlife rescue group is a good option. Typically, they will come pick up the bird or ask you to bring it in. If it's a pet bird or you suspect it belongs to someone else, take it to your local vet for treatment.
Drop a net or towel over the bird to capture it. Hold small birds in one hand between your fingers. Use 2 hands with large birds if you must handle one. Grip the bird firmly but don't restrict its breathing. Wrap the bird in a towel if you are having trouble restraining it. Handle the bird as little as possible to reduce stress. Put the bird in a well-ventilated box. Use darkness to reduce stress and shock. Cover the holes with fabric when transporting the bird. Take the bird to the veterinarian or call a rescue group.