Most normal pet birds never need to have their beaks trimmed. If the beak is actually overgrowing, it could be the result of an injury or deformity, mites, or disease. I recommend that you take the bird to an avian veterinarian for a checkup to see if a cause of the beak overgrowth can be determined.
If you do attempt to trim the beak yourself, be sure you do not hold the bird too tightly, because if you compress his chest he may not be able to breathe. If the beak is very long and curving around under the lower beak, then you can use a claw trimmer on the tip or fingernail trimmers on just the tip. After that, I would suggest using a nail file to gently sand the beak back into proper conformation. Only trim the very tip and use a nail file for the remainder - it would be better to leave him with a bit too much beak than to take too much off.
Hope that helps.