Do fingernails grow from the tip or the base?

Fingernails grow from beneath the nail fold (the flap of skin just below the white, semicircular part of the nail plate) and grow up towards the tip of the finger. If you think about cutting your fingernails, you cut them at the tip as they grow outward. It takes 3 to 6 months for the fingernail to grow from its base to the tip of the finger.

Each nail begins growing out of the root of the nail called the matrix. The matrix constantly makes new cells. These new cells force the old ones to get packed together and pushed up through the skin. By the time the nail pokes out of the skin (where you can see it), those cells are dead. That's why it doesn't hurt to cut your nails. Fingernails grow very slowly; a fingernail will take 6 months to grow back. Fingernails grow faster on your larger fingers and on your right hand if you're right-handed, and your left hand if you're left-handed. They grow faster during the day and in the summer.

https://www.aad.org/public/kids/nails/how-nails-grow
http://kidshealth.org/en/kids/your-nails.html