In general, canaries don’t need their nails to be clipped. When this happens, it is basically due to their habitat being too small or that it constantly supports its fingers on a wire structure.
If nail clipping is necessary, perform it as following:

• Wash the animals feet with soap and water
• Place nails in front of an intense light source. This way you will see a small and thin vein inside the nail.
• With sharp scissors, cut the tip of the nails leaving a few millimeters between the nail and the end of the vein.

You must pay special attention on the vain, avoiding it since it may bleed swelling the animal’s feet. If you are uncertain the first time, turn to a veterinary or experienced breeder for guidance.