How does a body on the surface of the earth apply a force on the ground? Since neither the body nor the surface of the earth is in motion, there is no acceleration and, hence, there can be no force because force equals mass times acceleration.
You're right, there is no acceleration thus the net force applied to the object is zero. Still you can decompose all the contributions to such net force and see that they are different from zero.
For example you have the weight of the object (or the gravitational pull of that object) does not vanish because the acceleration is zero, but is compensated with the force on the surface of the Earth in such a way that the net force is zero.