As a mass is introduced into a system (such as the Earth) the gravitational field that is created points towards the mass. 

   Why is this? well mathematically the answer is simple, because the field equation is nothing but products (multiplication) all with positive values. 

 Conceptually the reason why the field lines point inward is that gravitational fields are potential for a force.  A single mass creates field two masses create a force.  The potential force (gravitational field) should be in the direction of the attractive force of gravity, if you drop a ball above the Earth (regardless of the height) it is pulled toward the Earth.

Sir Isaac Newton's law of universal gravitation (i.e. the law of gravity) can be restated into the form of a gravitational field. Instead of calculating the forces between two objects every time, we instead say that an object with mass creates a gravitational field around it. The gravitational field is defined as the force of gravity at a given point divided by the mass of an object at that point.

This equation depicts a vector field around M which is always directed toward it, with a value equal to an object's gravitational acceleration within the field. The units of the gravitational field are m/s^2.

Definition provided by About.com

One mass

Because of the vector nature of gravity, the gravitational field created by a mass is a vector field.  Like all vectors, vector fields are also additive. Mapping a single mass we get a vector field we get the following image. 

    Remember that the strength of the gravitational field is proportional to 1/r^2.  That means if we double the distance away from a mass then the strength of the field drops by a 1/4, triple the distance the field strength is 1/9 it's original strength.  

Two or more masses 

Then when another mass is introduced, the fields created from the new mass interacts with the old field.  The field in between the points gets weaker, and a certain point the field goes to zero.  While in the space beyond the two points the field gets stronger.  Introducing a third mass, the regions between the masses the field gets weaker even still, outside slightly stronger.

Hollow Earth 

If you continue to bring in more and more mass you will create a hollow sphere (like a tennis ball) the hallow region inside the sphere.  The gravitational field goes to zero, meaning there is no chance for any gravitational force inside the sphere.  But outside the sphere the gravitational field is strong.  But how strong? 

This is how you can find out how.  Inside the ball the field is zero, outside the field is Gm/r^2 where m is the total of the mass of the ball, r is the average distance from each mass to where you want the measure the field.  But here is the cool part, the average distance is from the center of the ball to where you wanted to measure the field 

Science Fiction Folly  

  A Dyson sphere is a hypothetical megastructure originally described by Freeman Dyson. Such a "sphere" would be a system of orbiting solar power satellites meant to completely encompass a star and capture most or all of its energy output. Dyson speculated that such structures would be the logical consequence of the long-term survival and escalating energy needs of a technological civilization, and proposed that searching for evidence of the existence of such structures might lead to the detection of advanced intelligent extraterrestrial life.

A Dyson "sphere" is an impractical construct, why?