This may not be what you want to hear, but the best way to handle it is to leave it alone. Take it from me. I bit my nails for 18 years. I chewed them until they bled. When they were down to the quick, I chewed the skin around the nails. When that was too chewed up, I bit the inside of my cheeks until those bled. By then the fingers had healed a bit, so I would start in on them again.
My parents and grandparents tried everything to get me to stop: bitter nail polish, the promise of fabulous rewards, gloves, pretty false nails, punishment, sticker charts. Everything.
Nothing worked. And you know what? All the pressure to stop biting my nails just stressed me out and made me bite my nails even more obsessively.
By the time I got to high school, they had given up, and left me alone. And then, my senior year, I woke up one day and I *didn't need to bit my nails anymore*. Something just switched off. I didn't need that as a comfort mechanism. I outgrew it. I'm 30 years old now with long, strong, gorgeous nails that frequently get compliments from other ladies wanting to know where I get them done. (I don't) Do I still bite? Eh... not really. I do "trim" them with my teeth. After 18 years of practice, I'm unbelievably accurate, moreso than any clipper would be. Sometimes I "feel" them with my teeth. But I don't need to bite and chew anymore.
I would like for you to ask yourself this: Why is it important to you that your child stop biting his or her nails? Hygiene? Institute a frequent hand-washing policy. Is he hurting himself like I used to? Remind him about not biting to the quick and encourage frequent handwashing to keep infections at bay. Is it that chewed nails are ugly? Eh.. so what? They're her hands, right? People aren't going to judge your kid by his/her fingernails. Does it just bug you? Let it go or ask him to do it in private.
Nail biting is a pretty innocuous habit. I say, worry about the bigger stuff.