First off, I do not use my nail to open the clasp on a necklace. My manicurist would hurt me... she says "Nails are not tools. Nails are not tools. Repeat after me, nails are not tools." Using your nails will create teeny tiny dents in the edge of your nail that will lead to chipped polish and cracked nails eventually. Nails are not tools.
I use the side of my index finger. The secret for me is to hold the ends of the necklace between my thumb and index finger, the clasp part between my right hand thumb and index finger and the loop between my left hand thumb and index finger. Holding the clasp where you can see it, open the clasp, and holding it open bring the loop inside of the clasp then bring it out, then put it inside then bring it out. Do that several times to get a feel for it. Then without over thinking it, still holding the clasp open with your thumb and index finger, place the necklace around your neck, place the loop inside of the clasp exactly as you've just been getting a feel for, then release the clasp. Presto!
You go girl!
Miharu