I clip my own birds nails, and it's infinitely easier if you can find a second pair of hands to help.
Get them to hold the bird in a towel (or in their hands if the bird isn't bitey) and you can hold the toes as you clip the nails. I find using a mini pair of human nail clippers to be easiest. If your birds are nice they'll have lovely pink toenails and you'll be able to see the quick to avoid it (the vein in their nail):
If your bird is a butthead then it'll have black nails:
In which case you would just trim the very tip.
Have some flour ready and a towel/tissue to apply pressure if you cut a little too far. I've never had a toenail gush blood, so you would have to do a bit of a hack job to cause any real harm.