Watch Out For Nail Over-Growth
For some finches, toenails may grow very quickly. Many bird owners use sanded perches or natural wood to keep finch nails short. Sanded perches can harm your pet's sensitive feet, though, and natural wood perches can be expensive. Some birds' nails will grow out regardless of these measures, as well.
Finch toenails should resemble slight crescents; if they are too long or even beginning to curl in on themselves, they may get caught on the bars of the birdcage or other hazards. Finches are not very smart in a crisis, and a finch with its toes caught may just flail and pull until something breaks in an effort to escape. Damage from such an accident may include broken bones, wings, toenails, and potentially fatal blood loss.
If your pet's nails are getting too long, there are several ways to remedy the issue. The most reliable way to shorten them is to take the birds to a trained vet or groomer who offers the service. Another safe, if laborious, way to shorten the nails is to file them down slowly until they are a safe length.
If you are confident in your abilities, you can try to clip the nails yourself. Be mindful of the "quick", which is the blood supply of the nail. If you nick it, the finch may bleed to death in a manner of minutes. Corn starch can be pushed inside of the nail in the event of such an accident in order to stem the bleeding. A freshly snuffed match can also be pressed into the nail tip in order to cauterize the wound.
Regardless of the method you choose, quick action may be necessary to prevent permanent damage or even the death of your pet. If you doubt your abilities, it is always a good idea to take your bird to a professional.