Consult your avian veterinarian for help during the first nail trim.
To safely trim nails, some restraint is going to be necessary. A towel is preferred, but do not frighten your bird by suddenly pouncing on it from behind. Get expert instruction on how to correctly restrain your bird.
Never start without having some method (s) available for controlling bleeding if an accident should occur. Styptic powders can be applied to the bleeding end of a toe nail (but should not be used elsewhere on birds).
Use a sharp pair of trimmers (or a grinding bit on a Dremel tool) and good lighting.
On pale-colored nails, you should be able to see the nail go 'clear' near the tip, beyond the base where the quick lies. Cut in the clear area, removing the hooked and sharp tip.
On dark nails, visualizing the end of the quick will not be possible. Cut only the thin, sharp hooked tip, or use a grinding tool.
Watch the bird carefully for any signs of distress, and release the bird between feet or even after several toes have been trimmed. This is an important rule to follow if you have not trimmed nails before on that particular bird, or if the bird is struggling.
Try and make the whole experience as pleasant as possible. Once the bird is well used to the experience, longer sessions can be used.