The definitive word:

You can basically consider the Earth to be of uniform density for our purposes. As you headed toward the center of the Earth, the acceleration due to gravity would decrease linearly according to the equation:

a = G*4/3*pi*r*rho

Where rho is the density and r is the radius.

If they were halfway to the core then they should experience half the gravity. At the core (r=0) there would be no acceleration due to gravity at all.