You're thinking of a formula that says that the gravitational field falls off as the inverse of the square of the distance from an object. That formula only applies to point-like objects. When you have an extended object, you need to consider two complications:
1. The distances to different parts of the object are different.
2. The directions to different parts of the object are different, so the fields contributed don't all point the same way.
Calculating the net force then requires some effort. It was to solve this problem that Newton invented integral calculus.
For spherical shells, it turns out that the field outside the shell looks just the same as if all the mass were right at the middle. However, inside the shell it gives a field of zero. Right at the middle of the earth, you're inside all the shells, so the field is zero.
Of course, as we argued before, you know by symmetry that that has to be the answer.
(published on 10/05/12)